

































































Glass TA 5 
Book _l£) 2,9 


1 3 70 











I 

ELEMENTS 


SURVEYING, 

AND 

NAVIGATION, 

WITH DESCRIPTIONS OF THE INSTRUMENTS AND THE 

NECESSARY TABLES. 


BY CHARLES DAYIES, LL. D., 

i' 

' % 

AUTHOR OF ARITHMETIC, ALGEBRA, PRACTICAL MATHEMATICS FOR PRACTICAL MEN, 
ELEMENTS OF DESCRIPTIVE GEOMETRY, SHADES, SHADOWS, AND PER¬ 
SPECTIVE, ANALYTICAL GEOMETRY, DIFFERENTIAL AND 
INTEGRAL CALCULUS. 


REVISED EDITION. 


A. S. BARNES & COMPANY, 
NEW YORK AND CHICAGO. 




1870 




Babies’ > y 

®0urse juf IPdjjfmalus, 

Babies’ ^primary? Arithmetic and 2Table=33oolt—Designed for Beginners; 
containing the elementary tables of Addition, Subtraction, Multiplication, 
Division, and Denominate Numbers ; with a large number of easy and prac¬ 
tical questions, both mental and written. 

Babies’ jFirst Wessons tti Arithmetic—Combining the Oral Method with the 
Method of Teaching the Combinations of Figures by Sight. 

Babies’ intellectual Arithmetic—An Analysis of the Science of Numbers, with 
especial reference to Mental Training and Development. 

Babies* Xcb) School Arithmetic—Analytical and Practical. 

Hey? to Babies’ Xcto School Arithmetic. 

Babies* (Grammar of Arithmetic—An Analysis of the Language of Numbers 
and the Science of Figures. 

Babies’ Xcto SSnibersity? Arithmetic—Embracing the Science of Numbers, and 
their Applications according to the most Improved Methods of Analysis and 
Cancellation. 

Hey? to Babies’ Xeto ©taibersity? Arithmetic. 

Babies* Hlementary? Algebra—Embracing the First Principles of the Science. 

Hey? to Babies* Blemeutaru Algebra. 

Babies* Elementary? (Geometry? and trigonometry?—With Applications in 
Mensuration. 

Babies’ practical Mathematics—With Drawing and Mensuration applied to 
the Mechanic Arts. 

Babies* Elnlbersity? Algebra—Embracing a Logical Development of the 
Science, with graded examples. 

Babies’ Bourbon’s Algebra—Including Sturm’s and Horner’s Theorems, 
and practical examples. 

Babies* Hcgenbre’s (Geometry? anb trigonometry?— Revised and adapted to 
the course of Mathematical Instruction in the United States. 

Babies’ Elements of Sutbeyjlng and Xablgatlon—Containing descriptions 
of the Instruments and necessary Tables. 

Babies* Analytical (Geometry?—Embracing the Equations of the Point, the 
Straight Line, the Conic Sections, and Surfaces of the first ind second order. 

Babies' Bifferential and integral Calculus. 

Babies’ Bescrlptibe (Geometry?—With its application to Spherical Trigonome¬ 
try, Spherical Projections, and Warped Surfaces. 

Babies* Sbabes, Sbabotos, and Jlcrspectibe. 

Babies’ 3Logic anb utility? of Mathematics—With the best methods of In¬ 
struction Explained and Illustrated. 

Babies’ anb ^celt’s Mathematical Bfctlonary? anb Cy?clopeb!a of Matbe* 
mat'eal Science—Comprising Definitions of all the terms employed in 
Mathematics—an Analysis of each Branch, and of the whole, as forming a 
single Science. 


Entered according to Act of Congress, in the year one thousand eight hundred and fifty, 
three, by Charles Davies, in the Clerk’s Office oi the District Court of the Uuited States 
for the Southern District of New York. 


William Denyse, Stereotyper and Eleotrotypep., 1S3 William Street, New York. 



- 9 75 , 3 , 







ib,1/- 


i 


PREFACE. 


The Elements of Surveying, first published in 1830, 
was designed as a text-book for the pupils of the Military 
Academy, and in its preparation little regard was had to 
the supposed wants of other institutions. 

The work, however, was received by the public with 
more favor than was anticipated, and soon became a lead¬ 
ing text-book in the Colleges, the Academies, and the 
higher grade of Schools. 

For the purpose of adapting it, more fully, to the sup¬ 
posed wants of these institutions many changes have been 
made, since its first publication, and the present edition 
will be found to differ, in many respects, from those which 
have preceded. 

It has been the intention to begin with the very ele¬ 
ments of the subject, and to combine those elements in 
the simplest manner, so as to render the higher branches 
of plane surveying comparatively easy. All the instru¬ 
ments needed for plotting have been carefully described; 
and the uses of those required for the measurement of 
angles are fully explained. 

The conventional signs adopted by the Topographical 
Bureau, which are now used by the United States Engi¬ 
neers in all their Charts and Maps, are given in plates 
5 and 6. 

Should these signs be generally adopted in the country, 
it would give entire uniformity to all maps and delinea¬ 
tions of the ground, and would establish a kind of lan¬ 
guage by which all the peculiarities o c soil and surface 
could be accurately represented. 



IV 


PREFACE. 


A section has also been added on Geodesy. This 
branch of Surveying is extensively applied in the Coast 
Survey, and now forms an important element of a practi¬ 
cal or scientific education. 

A full account is also given of the manner of survey- 
ing the public lands; and, although the method is simple, 
it has, nevertheless, been productive of great results, by 
defining, with mathematical precision, the boundaries of 
lands in the new States, and thus settling their titles on 
an indisputable basis. 

This method was originated by Col. Jared Mansfield, 
whose great acquirements in science introduced him to the 
notice of President Jefferson, by whom he was appointed 
surveyor-general of the North-Western Territory. 

May it be permitted to one of his pupils, and a gradu¬ 
ate of the Military Academy, further to add, that at the 
organization of the institution in 1812, he was appointed 
Professor of Natural and Experimental Philosophy. This 
situation he filled for sixteen years, when he withdrew 
from the Academy to spend the evening of his life in re¬ 
tirement and study. His pupils, who had listened to his 
instructions with delight, who honored his learning and 
wisdom, and had been brought near to him by his kind 
and simple manners, have placed his portrait in the public 
library, that the institution might possess an enduring 
memorial of one of its brightest ornaments and distin¬ 
guished benefactors. 

At the solicitation of several distinguished teachers, there 
is added, in the present edition, an article on Plane Sail¬ 
ing, most of which has been taken, by permission of the 
author, from an excellent work on Trigonometry and its 
applications, by Professor Charles W. Hackley. 

Fishkill Landing, 

July, 1851. 


CONTENTS. 


BOOK I. 

SECTION I. 

PAGE. 

Of Logarithms,...... 9 

Table of Logarithms,_____ 11 

Multiplication by Logarithms,....... 15 

Division by Logarithms,___. ._____ 16 

Arithmetical Complement,...... 17 

SECTION II. 

r 

Geometrical Definitions,..._______ 19 

Geometrical Constructions,....... 25 

Description of Instruments,.... 25 

Dividers,..... 25 

Ruler and Triangle,_____ 25 

Scale of Equal Parts,________ 27 

Diagonal Scale of Equal Parts,___ 27 

Scale of Chords,......_.....__ 29 

Semicircular Protractor,. 30 

Sectoral Scale of Equal Parts,.... 30 

Gunter’s Scale,. 32 

Solution of Problems,........ 32 

SECTION III. 

Plane Trigonometry,..•. 38 

Division of the Circumference,...... 38 

Definitions of the Trigonometrical Lines,... 39 

Table of Natural Sines,....... 40 

Table of Logarithmic Sines,... 41 

Theorems,... 44 

Solution of Triangles,. 48 

Solution of Right-Angled Triangles,. 54 

A pplication to Heights and Distances,..... 55 





























VI 


CONTENTS. 


BOOK II. 

PLANE SURVEYING. 

SECTION I. 


Definitions,. 

Measurement of Lines and Angles,. 

Measures for Distances,. 

To Measure a Horizontal Line,. 

Measurement of Angles,. 

Of the Theodolite,. 

Verniers,. 

To Measure a Horizontal Angle with the Theodolite, 

To Measure a Vertical Angle,., 

Measurements with the Tape or Chain,. 

Surveying Cross,. 


SECTION II. 

Area, or Contents of Ground,. 

Of Laying out Land,. 


page. 
. 64 

. 66 
. 66 
. 67 
. 69 
. 69 
- 75 
. 77 
. 78 
. 79 
81 


85 

96 


SECTION III. 

The Circumferenter, or Surveyor’s Compass,. 98 

Surveying with the Compass, Definitions, etc.,. 99 

Field Operations,. 102 

Traverse Table,. 105 

Of Balancing the Work,. 109 

Of the Double Meridian Distances of the Courses,. 112 

Of Finding the Area,. 114 

First Method of Plotting,. 117 

Second Method of Plotting,. 117 

Problems,. 118 

Offsets,._. 122 

Of Supplying Omissions in the Field Notes,. 124 

To Determine the Angle between two Courses,. 126 

Of Dividing Land,. .27 

SECTION IV. 

Method of Surveying the Public Lands,. 131 

Variation of the Needle,.. 134 

Method of Ascertaining the Variations,._ 138 

To Find the True Meridian with the Theodolite,. 140 

To Find the True Meridian with the Compass,. 141 


































CONTENTS. 


Vil 


BOOK III. 

LEVELLING AND TOPOGRAPHICAL SURVEYING. 

SECTION I. 

PAGE. 

Of Levelling,. 145 

The Y Level,. 147 

The Water Level,. 150 

Levelling Staves,. 151 

Levelling in the Field,. 153 

Difference of Level between Two Points,. 153 

Example,. 154 

Levelling for Section,. 157 

Plotting the Section or Profile,. 158 

SECTION II. 

Topographical Surveying,. 159 

Field Notes,. 166 

Plotting the Work,. 167 

BOOK IY. 

GEODESIC, TRIGONOMETRIC, AND MARITIME 

SURVEYING. 

SECTION I. 

Geodesic and Trigonometric Surveying,. 172 

Preliminary Reconnoissance and Establishment of Signals,. 174 

Measurement of a Base Line,. 176 

Triangulation,. 178 

Filling up the Survey,. 181 

Use of the Compass,. 181 

The Plane Table—Its Uses,. 183 

To Measure a Horizontal Angle,. 185 

To Determine Lines in Extent and Position,. 185 

Of Changing the Paper,. 187 

Reduction to the Centre,. 189 

Spherical Excess,. 190 

Plotting the Triangulation,. 190 

The Circular Protractor,. 190 

To Lay off an Angle with the Protractor,. 193 

First Method of Plotting,. 193 

Second Method of Plotting,. 194 

Method of Chords,. 195 

To Lay off an Angle,. 196 

SECTION II. 

Maritime Surveying,. 197 


































viii 


CONTENTS.' 


BOOK y. 

OF NAVIGATION. 

SECTION I. 

Definitions.,.... . 



PAGE. 
. 201 


8ECTION II. 

Of Plane Sailing,...............—.... — ... 205 

SECTION III. 

Of Traverse Sailing,......___207 

Of Plotting,....209 


SECTION IV. 

Parallel Sailing,......211 

SECTION V. 

Middle Latitude Sailing,.......214 

Mercator’s Sailing,__________...... 218 

Mercator’s Chart,........ 221 


Line of Meridional Parts on Gunter’s Scale,...........____ 222 










ELEMENTS OE SURVEYING. 


BOOK I. 

SECTION I. 

OF LOGARITHMS. 

1. The bgarithm of a number is the exponent of the power 
to which it is necessary to raise a fixed number , in order to 
produce the first number. 

This fixed number is called the base of the system, and 
may be any number except 1: in the common system. 10 
is assumed as the base. 

2. If we form those powers of 10, which are denoted 
by entire exponents, we shall have 

10°= 1 10* = 10 , 10 3 = 1000 

10 5 = 100, 10 4 = 10000, &c., &c., 

From the above table, it is plain, that 0, 1, 2, 3, 4, &c., 
are respectively the logarithms of 1, 10, 100, 1000, 10000,' 
&c.; we also see, that the logarithm of any number be¬ 
tween 1 and 10, is greater than 0 and less than 1: thus* 

log 2 = 0.301030. 

The logarithm of any number greater than 10, and loss 
than 100, is greater than 1 and less than 2: thus, 

log 50 = 1.698970. 

The logarithm of any number greater than 100, and 
less than 1000, is greater than 2 and less than 3: thus, 

log 126 = 2.100371, &c. 



10 


ELEMENTS OF SURVEYING [BOOK I 


If the above principles be extended to other numbers* 
it will appear, that the logarithm of any number, not an 
exact power of ten, is made up of two parts, an entire and 
a decimal part. The entire part is called the characteristic 
of the logarithm , and is always one less than the number of 
places of figures in the given number. 

3. The principal use of logarithms, is to abridge nu¬ 
merical computations. 

Let M denote any number, and let its logarithm be 
denoted by m; also let N denote a second number whose 
logarithm is n; then, from the definition, we shall have, 

10 m = M (1) 10" = N (2). 

Multiplying equations (1) and (2), member by member 
We have, 

10 m + n = MxN or, m + ?i=log (. M X N) ; hence, 

The sum of the logarithms of any two numbers is equal to 
the logarithm of their product 

4. Dividing equation (1) by equation (2), member by 
member, we have, 

,n_n M M 

10 = or, m — n — log ~^ \ hence, 

The logarithm of the quotient of two numbers, is equal to 
itie logarithm of the dividend diminished by the logarithm of 
the divisor. 

5. Since the logarithm of 10 is 1, the logarithm of the 
product of any number by 10, will be greater by 1 than the 
logarithm of that number ; also, the logarithm of the quotient 
of any number divided by 10, will be less by 1 than the 
logarithm of that number. 

Similarly, it may be shown that if any number be mul 
tiplied by one hundred, the logarithm of the product will 
be greater by 2 than the logarithm of that number; and 
if any number be divided by one hundred, the logarithm 
of the quotient will be less by 2 than the logarithm of 
that number, and so on. 


SEO. I] 


LOGARITHMS 


11 


EXAMPI.ES. 


log 327 is 2 514548 

log 32.7 “ 1.514548 

log 3.27 “ 0.514548 

log .327 “ 1.514548 

log .0327 “ 2.514548 


From the above examples, we see, that in a number 
composed of an entire and decimal part, we may change 
the place of the decimal point without changing the deci 
mal part of the logarithm; but the characteristic is dimin¬ 
ished hy 1 for every place that the decimal point is removed tc 
the left . 

In the logarithm of a decimal, the characteristic becomes 
negative, and is numerically 1 greater than the number of 
ciphers immediately after the decimal point. The negative 
sign extends only to the characteristic, and is written over 
it, as in the examples given above. 

TABLE OF LOGARITHMS. 

0. A table of logarithms, is a table in which are writ* 
ten the logarithms of all numbers between 1 and some 
given number. The logarithms of all numbers between 1 
and 10,000 are given in the annexed table. Since rules 
have been given for determining the characteristics of 
logarithms by simple inspection, it has not been deemed 
necessary to write them in the table, the decimal part 
only being given. The characteristic, however, is given 
for all numbers less than 100. 

The left hand column of each page of the table, is the 
column of numbers, and is designated by the letter 1ST; 
the logarithms of these numbers are placed opposite them 
on the same horizontal line. The last column on each 
page, headed D, shows the difference between the loga¬ 
rithms of two consecutive numbers. This diffeience is 
found by subtracting the logarithm under the column 
headed 4, from the one in the column headed 5 in the 
same horizontal line, and is nearly a mean of the differ¬ 
ences of any two consecutive logarithms on this line. 


12 


ELEMENTS OF SURVEYING. 


[BOOK J 


To find , from the table, the logarithm of any number. 

7. If the number is less than 100, look on the first page 
of the table, in the column of numbers under 1ST, until the 
number is found: the number opposite is the logarithm 
sought: Thus, 

log 9 = 0.954243. 

When the number is greater than 100 and less than 10000. 

8. Find in the column of numbers, the first three figures 
of the given number. Then pass across the page along a 
horizontal line until you come into the column under the 
fourth figure of the given number: at this place, there are 
four figures of the required logarithm, to which two figures 
taken from the column marked 0, are to be prefixed. 

If the four figures already found stand opposite a row 
of six figures in the column marked 0, the two left hand 
figures of the six, are the two to be prefixed; but if they 
stand opposite a row of only four figures, you ascend the 
column till you find a row of six figures; the two left 
hand figures of this row are the two to be prefixed. It 
you prefix to the decimal part thus found, the characteristic, 
you will have the logarithm sought: Thus, 

log 8979 = 3.953228 
log .08979 = 2.953228 

If, however, in passing back from the four figures found 
to the 0 column, any dots be met with, the two figures 
to be prefixed must be taken from the horizontal line di¬ 
rectly below: Thus, 

log 3098 = 3.491081 
log 30.98 = 1.491081 

If the logarithm falls at a place where the dots occur 
0 must be written for each dot, and the two figures to be 
prefixed are, as before, taken from the line below: Thus, 

log 2188 = 3.340047 
log .2188 = 1.340047 


SEC. L] 


LOGARITHMS. 


X3 


When the number exceeds 10,000. 

9. The characteristic is determined by the rules already 
given. To find the decimal part of the logarithm: place 
a decimal point after the fourth figure from the left 
hand, converting the given number into a whole number 
and decimal. Find the logarithm of the entire part by the 
rule just given, then take from the right hand column of 
the page, under D, the number on the same horizontal 
line with the logarithm, and multiply it by the decimal 
part; add the product thus obtained to the logarithm al¬ 
ready found, and the sum will be the logarithm sought. 

If, in multiplying the number taken from the column 
D, the decimal part of the product exceeds .5, let 1 be 
added to the entire part; if it is less than .5, the decimal 
part of the product is neglected. 

EXAMPLE. 

1. To find the logarithm of the number 672887. 

The characteristic is 5.; placing a decimal point after 
the fourth figure from the left, we have 6728.87. The 
decimal part of the log 6728 is .827886, and the corres¬ 
ponding number in the column D is 65; then 65x.87= 
56.55, and since the decimal part exceeds .5, we have 57 
to be added to .827886, which gives .827943. 

Hence, log 672887 = 5.827943 

Similarly, log .0672887 = 2.827943 

The last rule has been deduced under the supposition 
that the difference of the numbers is proportional to the 
difference of their logarithms, which is sufficiently exact 
within the narrow limits considered. 

In the above example, 65 is the difference between the 
logarithm of 672900 and the logarithm of 672800, that is, 
it is the difference between the logarithms of two numbers 
which differ by 100. 

We have then the proportion 

100 : 87 : : 65 : 56.55, 

hence, 56.55 is the number to be added to the logarithm 
before found. 


14 


ELEMENTS OF SURVEYING. 


[BOOK I. 


To find from the table the number corresponding to a given 

logarithm. 

10. Scarcli in the columns of logarithms for the decimal 
part of the given logarithm: if it cannot be found in the 
table, take out the number corresponding to the next less 
logarithm and set it aside. Subtract this less logarithm 
from the given logarithm, and annex to the remainder as 
many zeros as may be necessary, and divide this result by 
the corresponding number taken from the column marked 
D, continuing the division as long as desirable: annex the 
quotient to the number set aside. Point off, from the left 
hand, as many integer figures as there are units in the 
characteristic of the given logarithm increased by 1; the 
result is the required number. 

If the characteristic is negative, the number will be 
entirely decimal, and the number of zeros to be placed at 
the left of the number found from the table, will be equal to 
the number of units in the characteristic diminished by 1. 

This rule, like its converse, is founded on the supposi¬ 
tion that the difference of the logarithms is proportional 
to the difference of their numbers within narrow limits. 

EXAMPLE. 

1. Find the number corresponding to the logarithm 
3.233568. 

The decimal part of the given logarithm is .233568 

The next less logarithm of the table is .233504, 

and its corresponding number 1712. - 

Their difference is - - - 64 

Tabular difference 253)6400000(25 

Hence, the number sought 1712.25. 

The number corresponding to the logarithm 3.233568 
is 00171225. 

2. What is the number corresponding to the logarithm 

2.785107? Ans. .06101084. 

3. What is the number corresponding to the logarithm 

1.846741? Ans. .702653. 



8EC. I] 


LOGARITHMS. 


15 


MULTIPLICATION BY LOGARITHMS. 

11. When it is required to multiply numbers by means 
of their logarithms, we first find from the table the loga¬ 
rithms of the numbers to be multiplied; we next add 
these logarithms together, and their sum is the logarithm 
of the product of the numbers (Art. 3). 

The term sum is to be understood in its algebraic 
sense; therefore, if any of the logarithms have negative 
characteristics, the difference between their sum and that 
of the positive characteristics, is to be taken; the sign of 
the remainder is that of the greater sum. 

* 

EXAMPLES. 

1. Multiply 23.14. by 5.062. 

log 23.14 = 1.864363 
log 5.062 = 0.704322 

Product, 117.1347 . . . 2.068685 

2 . Multiply 3.902, 597.16, and 0.0314728 together. 

log 3.902 = 0.591287 
log 597.16 = 2.776091 
log 0.0314728 = 2.497936 

Product, 73.3354 .... 1.865314 

Here, the 2 cancels the + 2, and the 1 carried from 
die decimal part is set down. 

3. Multiply 3.586, 2.1046, 0.8372, and 0.0294 together. 

log 3.586 = 0.554610 
log 2.1046 = 0.323170 
log 0.8372 = 1.922829 
log 0.0294 = 2.468347 

Product, 0.1857615 . . 1.268956 

In this example the 2, carried from the decimal part, 
cancels 2, an 1 there remains 1 to be set down. 








16 


ELEMENTS OF SURVEYING. 


[BOOK 1 


DIVISION OF NUMBERS BY LOGARITHMS. 

12. When it is required to divide numbers by means 
of their logarithms, we have only to recollect, that the 
subtraction of logarithms corresponds to the division of 
their numbers (Art. 4). Hence, if we find the logarithm 
of the dividend, and from it subtract the logarithm of thd 
divisor, the remainder will be the logarithm of the quotient. 

This additional caution may be added. The difference 
of the logarithms, as here used, means the algebraic differ¬ 
ence; so that, if the logarithm of the divisor have a nega¬ 
tive characteristic, its sign must be changed to positive, 
after diminishing it by the unit, if any, carried in the sub¬ 
traction from the decimal part of the logarithm. Or, if 
the characteristic of the logarithm of the dividend is nega¬ 
tive, it must be treated as a negative number. 

EXAMPLES. 

1. To divide 24163 by 4567. 

log 24163 = 4.383151 
log 4567 = 3.659631 

Quotient, 5.29078 . . 0.723520 


2. To divide 0.06314 by .007241. 

log 0.06314 = 2.800305 
log 0.007241 = 3.859799 

Quotient, 8.7198 . . 0.940506 


Here, 1 carried from the decimal part to the 3, changes 
it to 2, which being taken from 2, leaves 0 for the cha¬ 
racteristic. 

3. To divide 37.149 by 523.76. 

log 37.149 = 1.569947 
log 523.76 = 2.719133 


Quotient, 0.0709274 . 2.850814 








SEC. IJ 


LOGARITHMS. 


IT 


4 To divide 0.7438 by 12.9476. 

log 0.7438 = 1.871450 
log 12.9476 = 1.112189 

Quotient, 0.057447 . . 2.759267 

Here, tbe 1 taken from 1, gives 2 for a result, as set; 

down. 

ARITHMETICAL COMPLEMENT. 

13. The Arithmetical complement of a logarithm is the 
number which remains after subtracting the logarithm 
from 10. 

Thus, 10 - 9.274687 = 0.725313. 

Hence, 0.725313 is the arithmetical complement 

of 9.274687. 

14. We will now show that, the difference between two 
logarithms is truly found , by adding to the first logarithm the 
arithmetical complement of the logarithm to be subtracted , and 
then diminishing the sum by 10. 

Let a — the first logarithm, 

b — the logarithm to be subtracted, 
and c= 10 — b — the arithmetical complement of b. 

How the difference between the two logarithms will be 
expressed by a —b. 

But, from the equation c = 10 — b, we have 

c—10'= —a, 

hence, if we place for — b its value, we shall have 

a — b = a + c —10, 

which agrees with the enunciation. 

When we wish the arithmetical complement of a loga¬ 
rithm, we may write it directly from the table, by subtract • 
ing the left hand figure from 9, then proceeding to the right , 
subtract each figure from 9 till we reach the last significant 
figure, which must be taken from 10: this will be the same 
as talcing the logarithm from 10. 

2 




18 


ELEMENTS OF SURVEYING 


[BOOK I 


EXAMPLES. 

1. From 8.274107 take 2.104729. 

By common method. By cirith. comp. 

3.274107 3.274107 

2.104729 its ar. comp. 7.895271 

Diff. 1.169378 Sum 1.169378 after sub 

tracting 10. 

Hence, to perform division by means of the arithmetical 
complement, we have the following 


RULE. 

To the logarithm of the dividend add the arithmetical com¬ 
plement of the logarithm of the divisor: the sum , after sub¬ 
tracting 10, tvill he the logarithm of the quotient. 

EXAMPLES. 

1. Divide 327.5 by 22.07. 

log 327.5 . 2.515211 

log 22.07 ar. comp. 8.656198 

Quotient, 14.839 . . . 1.171409 

2. Divide 0.7438 by 12.9476. 

log 0.7438 .... 1.871456 
log 12.9476 ar. comp. 8.887811 

Quotient, 0.057447 . . . 2.759267 

In this example, the sum of the characteristics is 8, 
from which, taking 10, the remainder is 2. 

3. Divide 37.149 by 523.76. 

log 37.149 .... 1.569947 

log 523.76 ar. comp. 7.280867 

Quotient, 0.0709273 . . 2.850814 














SEC. II] 


GEOMETRICAL DEFINITIONS. 


19 


4. Divide 0.875 by 25. 

5. Divide 3.1416 by .944. 

6. Divide 2756 by 327. 

7. Divide 672859 by 0.09657. 


Ans. 0.035. 
Ans . 3.3279. 
.4rcs. 8.4281. 
Am. 6967580.04. 


SECTION IL 

GEOMETRICAL DEFINITIONS AND CONSTRUCTIONS. 

1. Extension lias three dimensions, length, breadth, 
and thickness. 

2. Geometry is the science which has for its object: 

1st. The measurement of extension; and 2dly. To dis* 

cover, by means of such measurement, the properties and 
relations of geometrical figures. 

3. A Point is that which has place, or position, but 
not magnitude. 

4. A Line is length, without breadth or thickness. 

5. A Straight Line is one which 
lies in the same direction between any 
two of its points. 

6. A Broken Line is one made up 
of straight lines, not lying in the same 
direction. 

7. A Curve Line is one which 
changes its direction at every point. 

The word line when used alone, will designate a straight 
line; and the word curve , a curve line. 

8. A Surface is that which has length and breadth 
without thickness. 






20 


ELEMENTS OF SURVEYING. 


[BOOK I. 


9. A Plane is a surface, such, that if any two of its 
points be joined by a straight line, such line will be wholly 
in the surface. 

10. Every surface, which is not a plane surface, or com¬ 
posed of plane surfaces, is a curved surface. 

11. A Solid, or Body is that which has length, breadth, 
and thickness: it therefore combines the three dimensions 
of extension. 

12. An Angle is the portion of a plane included be¬ 
tween two straight lines which meet at a common point 
The two straight lines are called the sides o/ the angle, 
and the common point of intersection, the vertex. 

Thus, the part of the plane includ¬ 
ed between AB and A G is called an 
angle : AB and A G are its sides, and A s' 

its vertex. s' 

An angle is sometimes designated -— b 

simply by a letter placed at the vertex, 
as, the angle A ; but generally, by three letters, as, the 
angle BAG or GAB \ —the letter at the vertex being always 
placed in the middle. 

13. When a straight line meets an¬ 
other straight line, so as to make the 
adjacent angles equal to each other, 
each angle is called a right angle ; and 

the first line is said to be perpendicu - __, 

lar to the second. 


14. An Acute Angle is an angle 
less than a right angle. 



15. An Obtuse Angle is an angle 
greater than a right angle. 



1 


t 









SEC. II.] 


GEOMETRICAL DEFINITIONS 


23 


16 . Two straight lines are said to 

be parallel , when being situated in _- 

the same plane, they cannot meet, how 
far soever, either way, both of them 
be produced. 

17. A Plane Figure is a portion of a plane terminal 
ed on all sides by lines, either straight or curved. 

18. A Polygon, or rectilineal fig¬ 
ure, is a portion of a plane terminat¬ 
ed on all sides by straight lines. 

The sum of the bounding lines is 
called the perimeter of the polygon. 



19. The polygon of three sides, the simplest of all, is 
called a triangle; that of four sides, a quadrilateral; that 
of five, a pentagon; that of six, a hexagon; that of seven, 
a heptagon; that of eight, an octagon; that of nine, an 
nonagon; that of ten, a decagon; and that of twelve, a 
dodecagon. 


20. An Equilateral polygon is one which has all its 
sides equal; an equiangular polygon, is one which has all 
its angles equal. 


21. Two polygons are mutually equilateral, when they 
have their sides equal each to each, and placed in the 
same order: that is to say, when following their bounding 
lines in the same .direction, the first side of the one is 
equal to the first side of the other, the second to the 
second, the third to the third, and so on. 

22. Two polygons are mutually equiangular, when every 
angle of the one is equal to a corresponding angle of the 

other, each to each. 

23. Triangles are divided into classes with reference 
both to their sides and angles. 

1. An equilateral triangle is one 
which has its three sides equal. 







22 


ELEMENTS OF SURVEYING. |BUOK i. 


2. An isosceles triangle is one which 
has only two of its sides equal. 



3. A scalene triangle is one which has 
its three sides unequal. 



4. An acute-angled triangle is one 
which has its three angles acute. 



5. A right-angled triangle is one which 
has a right angle. The side opposite the 
right angle is called the hypothenuse , and 
the other two sides, the hose and perpen¬ 
dicular. 

6. An obtuse-angled tnangle is one 
which has an obtuse angle. 


24. There are three kinds of Quadrilaterals: 




1. The trapezium , which has none of 
its sides parallel. 



2. The trapezoid , which has only two 
of its sides parallel. 



3. The parallelogram , which has its 
opposite sides parallel. 














SEC. II.J GEOMETRICAL DEFINITIONS. 


23 


25. There are four kinds of Parallelograms: 

1. The rhomboid, which has no right 
angle. 



2. The rhombus , or lozenge , which is 
an equilateral rhomboid. 



3. The rectangle , which is an equian¬ 
gular parallelogram, but not equilateral. 


4. The square , which is both equilat¬ 
eral and equiangular. 


A Diagonal of a figure is a line 
which joins the vertices of two angles 
not adjacent. 



EXPLANATION OF SIGNS. 

26. The sign = is the sign of equality; thus, the ex¬ 
pression A — B, signifies that A is equal to B. 

27. To signify that A is smaller than B, the expression 
A < B is used. 

28. To signify that A is greater than B , the expression 
A > B is used; the smaller quantity being always at the 
vertex of the angle. 

29. The sign -f is called, plus; it indicates addition. 









24 ELEMENTS OF SURVEYING. [BOOK I 

/ 

SO. Tlie sign — is called minus; it indicates subtraction: 
Thus, A A B, represents the sum of the quantities A 
and B; A — B represents their difference, or what remains 
after B is taken from A ; and A — B + C, or A + G — B ) 
signifies that A and G are to be added together, and that 
B is to be subtracted from their sum. 

31. The sign X indicates multiplication : thus A X B 
represents the product of A and B. 

The expression A X {BA C — D) represents the product 
of A by the quantity BaC—D. If AaB were to be 
multiplied by A — B + (7, the product would be indicated 
thus; 

(A+D)X(A-B+C), 

whatever is enclosed within the curved lines, being consid¬ 
ered as a single quantity. The same thing may also be 
indicated by a bar: thus, 

A + B + Ox D , 

denotes that the sum of A, B and C,\ is to be multiplied 
by D. 

32. A figure placed before a line, or quantity, serves 
as a multiplier to that line or quantity; thus, 3Ai? signi 
fies that the line AB is taken three times; \A signifies the 
half of the angle A. 

33. The square of the line AB is designated by AB '; 

— ^ 

its cube by AB . What is meant by the square and cube 
of a line is fully explained in Geometry. 

34. The sign ^ indicates a root to be extracted; thus, 

V2 means the square-root of 2; V A X B means the square 
root of the oroduct of A and B 






SEC. II] GEOMETRICAL CONSTRUCTIONS. 


25 


GEOMETRICAL CONSTRUCTIONS. 

35. Before explaining the method of constructing geo¬ 
metrical problems, we shall describe some of the simpler 
instruments and their uses. 


DIVIDERS. 



36. The dividers is the most simple and useful of the 
instruments used for drawing. It consists of two legs ba 
5c, which may be easily turned around a joint at b. 

One of the principal uses of this instrument is to lay 
off on a line, a distance equal to a given line. 

For example, to lay off on CD a distance equal to AB, 
For this purpose, place the forefin¬ 
ger on the joint of the dividers, and A\ - \B 

set one foot at A: then extend, with 

the thumb and other fingers, the Cl 'e~'/ D 

other leg of the dividers, until its foot reaches the point 
B. Then raise the dividers, place one foot at (7, and 
mark with the other the distance CE: this will evidently 
be equal to AB. 


RULER AND TRIANGLE. 



37. A Euler of convenient size, is about twent}^ inches 
in length, two inches wide, and a fifth of an inch in thick- 











26 


ELEMENTS OF SURVEYING. [BOOK I 

ness. It should be made of a bard material, perfectly 
straight and smooth. 

The hypothenuse of the right-angled triangle, which is 
used in connection with it, should be about ten inches in 
length, and it is most convenient to have one of the sides 
considerably longer than the other. We can solve, with 
the ruler and triangle, the two following problems. 


L Tc draw through a given point a line which shall be paral¬ 
lel to a given line. 

38. Let C be the given point, and AB the given line. 

Place the hypothenuse of the tri- c 

angle against the edge of the ruler, 

and then place the ruler and triangle _, 

on the paper, so that one of the 

sides of the triangle shall coincide exactly with AB: the 

triangle being below the line. 

Then placing the thumb and fingers of the left hand 
firmly on the ruler, slide the triangle with the other hand 
along the ruler until the side which coincided with AB 
reaches the point 0. Leaving the thumb of the left hand 
on the ruler, extend the fingers upon the triangle and hold 
it firmly, and with the right hand, mark with a pen or 
pencil, a line through C: this line will be parallel to AB. 

II. To draw through a given point a line which shall be per¬ 
pendicular to a given line. 

39. Let AB be the given line, and D the given point. 

Place the hypothenuse of the tri¬ 
angle against the edge of the ruler, as 

before. Then place the ruler and __ 

triangle so that one of the sides of A 
the triangle shall coincide exactly with the line AB. 
Then slide the triangle along the ruler until the other 
side reaches the point D: draw through D a right line, 
and it will be perpendicular to AB. 






8 E 0 . IIJ GEOMETRICAL CONSTRUCTION’S. 


27 


SCALE OF EQUAL PARTS, 


.1 .2 .. 1 . 4.5 .5 . 7.5 . 57 ) 


40. A scale of equal parts is formed by dividing a line 
of a given length into equal portions. 

If, for example, the line ab of a given length, say one 
inch, be divided into any number of equal parts, as 10, 
the scale thus formed, is called a scale of ten parts to the 
inch. The line ab, which is divided, is called the unit of 
the scale. This unit is laid off several times on the left 
of the divided line, and the points marked 1, 2, 3, &c. 

The unit of scales of equal parts, is, in general, either 
ail inch, or an exact part of an inch. If, for example, ab, 
the unit of the scale, were half an inch, the scale would 
be one of 10 parts to half an inch, or of 20 parts to the 
inch. 

If it were required to take from the scale a line equal 
to two inches and six-tenths, place one foot of the dividers 
at 2 on the left, and extend the other to .6, which marks 
the sixth of the small divisions: the dividers will then 
embrace the required distance. 


DIAGONAL SCALE OF EQUAL PARTS. * 


d J 1 _ C 




lull 1 1 III 


• oa 

1 L II 

lllll 


• 08 

T 

1 1 

n ii i i 


■07 

1 

J 1 1 1 II 1 1 


.06 

1 


1 1 1 1 1 1 1 


• 05 

1 


1*1 1 1 1 


.04 

H 


u r 


.03 

i 

1 

i i 

/ 1 1 


•02 

MM 



i r 


.0.1 

1 1 1 1 


i 

l 


2 I a .1 .2 .3.4 ,5 .6 .7 .S .9 b 

h £/ 


41. This scale is thus constructed. Take ab for the 
unit of the scale, which may be one inch, i, \ or J of an 
inch, in length. On ab describe the square abed. Divide 
the sides ah and dc each into ten equal parts. Draw of 
and the other nine parallels as in the figure. 

Produce ba to the left, and lay off the unit of the 
scale any convenient number of times, and mark the poinxs 



























28 


ELEMENTS OF SURVEYING. 


[BOOK 1 


1, 2, 3, &c. Then, divide the line ad into ten equal parts, 
and through the points of division draw parallels to ab, as 
in the figure. 

Now, the small divisions of the line ab are each one- 
tenth (.1) of ab; they are therefore .1 of ad, or 1 of ag 
or gh. 

If we consider the triangle adf we see that the base df 
is one-tenth of ad, the unit of the scale. Since the distance 
from a to the first horizontal line above ab , is one-tenth of 
the distance ad, it follows that the distance measured on that 
line between ad and af is one-tenth of df: but since one-tenth 
of a tenth is a hundredth, it follows that this distance is 
one hundredth (.01) of the unit of the scale. A like dis¬ 
tance measured on the second line will be two hundredths 
(.02) of the unit of the scale; on the third, .03 ; on the 
fourth, .04, &c. 

If it were required to take, in the dividers, the unit of 
the scale, and any number of tenths, place one foot of the 
dividers at 1, and extend the other to that figure between 
a and b which designates the tenths. If two or more 
units are required, the dividers must be placed on a point 
of division further to the left. 

When units, tenths, and hundredths, are required, place 
one foot of the dividers where the vertical line through 
the point which designates the units, intersects the line 
which designates the hundredths: then, extend the dividers 
to that line between ad and be which designates the tenths: 
the distance so determined will be the one required. 

For example, to take off the distance 2.34, we place 
one foot of the dividers at l, and extend the other to e 3 
and to take off the distance 2.58, we place one foot of the 
dividers at p and extend the other to q. 

Remark I. If a line is so long that the whole of it 
cannot be taken from the scale, it must be divided, and 
the parts of it taken from the scale in succession. 

Remark II. If a line be given upon the paper, its 
length can be found by taking it in the dividers and ap 
plying it to the scale. 


SEC. II.] 


GEOMETRICAL CONSTRUCTIONS 


29 


SCALE OF CHORDS. 



42. If) with, any radius, as AC, we describe the quad¬ 
rant CD, and then divide it into 90 equal parts, each part 
is called a degree. 

Through C, and each point of division, let a chord be 
drawn, and let the lengths of these chords be accurately 
laid off on a scale: such a scale is called a scale of chords. 
In the figure, the chords are drawn for every ten de¬ 
crees. 

The scale of chords being once constructed, the radius 
of the circle from which the chords were obtained, is 
known; for, the chord marked 60 is always equal to the 
radius of the circle. A scale of chords is generally laid 
down on the scales which belong to cases of mathematical 
instruments, and is marked cno. 


To lay off', at a given point of a line, with the sccde of chords , 

an angle equal to a given angle. 

48. Let AB be the line, and A the given point. 

Take from the scale the chord of 60 
degrees, and with this radius and the 
point A as a centre, describe the arc 
BC. Then take from the scale the 
chord of the given angle, say 80 de¬ 
grees, and with this line as a radius, and as a centre, 
describe an are cutting BC in C. Through A and C 
draw the line AC, and BAG will be the required angle. 



t 







80 


ELEMENTS OF SURVEYING. 


[BOOK 1 


SEMICIRCULAR PROTRACTOR. 
C 



44. This instrument is used to lay down, or protract 
angles. It may also be used to measure angles included 
between lines already drawn upon paper. 

It consists of a brass semicircle, ABO , divided to half 
degrees. The degrees are numbered from 0 to 180, both 
wavs; that is, from A to B and from B to A. The di- 
visions, in the figure, are made only to degrees. Thera* 
is a small notch at the middle of the diameter AB , which 
indicates the centre of the protractor. 

To lay off an angle with a Protractor. 

45. Place the diameter AB on the line, so that the 
centre shall fall on the angular point. Then count the 
degrees contained in the given angle from A towards i?, or 
from B towards J., and mark the extremity of the arc with 
a pin. Eemove the protractor, and draw a line through 
the point so marked and the angular point: this line will 
make with the given line the required angle. 


SECTORAL SCALE OF EQUAL PARTS. 























BEC. IL] GEOMETRICAL CONSTRUCTIONS. 


31 


46. The sector is an instrument generally made of ivory 
or brass. It consists of two arms, or sides, which open 
by turning round a joint at their common extremity. 

There are several scales laid down on the sector: those, 
however, which are chiefly used in drawing lines and 
angles, are, the scale of chords already described, and the 
scale of equal parts now to be explained. 

On each arm of the sector, there is a diagonal line 
that passes through the point about which the arms turn: 
these diagonal lines are divided into equal parts. 

On the sectors which belong to the cases of English 
instruments, the diagonal lines are designated by the letter 
Z, and numbered from the centre of the sector, 1, 2, 3, 4. 
5, 6, 7, 8, 9, 10, to the two extremities. On the sectors 
which belong to cases of French instruments, they are de¬ 
signated, “Les parties egales,” and numbered 10, 20, 30, 
40, &c., to 200. On the English sectors there are 20 equal 
divisions between any two of the lines numbered 1, 2, 3, 
&c., so that there are 200 equal parts on the scale. 

The advantage of the sectoral scale of equal parts, is 
this—• 

IVhen it is proposed to draw a line upon paper, on 
such a scale that any number of parts of the line, 40 for 
example, shall be represented by one inch on the paper, or 
by any part of an inch, take the inch, or part of the inch, 
from the scale of inches on the sector: then, placing one 
foot of the dividers at 40 on one arm of the sector, open 
the sector until the other foot reaches to the corresponding 
number on the other arm: then lay the sector on the table 
without varying the angle. 

Now, if we regard the lines on the sector as the sides 
of a triangle, of which the line 40, measured across, is the 
base, it is plain, that if any other line be likewise meas 
ui*ed across the angle of the sector, the bases of the tri 
angles, so formed, will be proportional to their sides. 
Therefore, if we extend the dividers from 50 to 50, this 
distance will represent a line of 50, to the given scale, 
and similarly for other lines. 


32 ELEMENTS OF SURVEYING. [BOOK 1. 

Let it now be required to lay down a line of sixty- 
seven feet, to a scale of twenty feet to the inch. 

Take one inch from tbe scale of inches: then place 
one foot of tbe dividers at tbe twentieth division, and 
open tbe sector until tbe dividers will just reach tbe twen¬ 
tieth division on tbe other arm: tbe sector is then set to 
tbe proper angle; after which tbe required distance to be 
laid down on tbe paper is found by extending tbe divi¬ 
ders from tbe sixty-seventh division on one arm, to tbe 
sixty-seventh division on tbe other. 

gunter’s scale. 

47. This is a scale of two feet in length, on tbe faces 
of which a variety of scales is marked. Tbe face on 
which tbe divisions of inches are made, contains, however, 
all tbe scales necessary for laying down lines and angles. 
These are, tbe scale of equal parts, tbe diagonal scale of 
equal parts, and tbe scale of chords, all of which have 
been described. 


SOLUTION OF PROBLEMS REQUIRING THE USE OF THE IN¬ 
STRUMENTS THAT HAVE BEEN DESCRIBED. 


L At a given point in a given straight line , to erect a perpm' 

dicular to the line. 

48. Let A be tbe given point, and BG tbe given line. 




From A lay off any two distances, 

AB and AC, equal to each other. 

Then, from tbe points B and G, as 
centres, with a radius greater than BA , 
describe two arcs intersecting each B A 
other in D: draw AD, and it will be tbe perpendicular 
required. 


IT. From a given point without a straight line , to let fall a 

perpendicular on the line . 

49. Let A be tbe given point, and BD tbe given line. 




SEC.IL] GEOMETRICAL CONSTRUCTIONS. 


33 


From the point i as a centre, 
with a radius sufficiently great, 
describe an arc cutting the line 
BD in the two points B and D: 
then mark a point E, equally dis¬ 
tant from the points B and D, 
and draw AE: AE will be the perpendicular required. 



III. At a point , in a given line , to make an angle equal to a 

given angle. 

50. Let A be the given point, AE the given line, and 
IKL the given angle. 

From the vertex K, as a 
centre, with any radius, describe 
the arc IL , terminating in the 
two sides of the angle. From 
the point A as a centre, with a distance AE equal to K1 ’ 
describe the arc ED; then take the chord LI, with which, 
from the point ^ as a centre, describe an arc cutting the 
indefinite arc DE\ in D; draw AD, and the angle EAD 
will be equal to the given angle K. 



IV. To divide a given angle, or a given arc t into two equal 

parts. 


51. Let C be the given angle, 
measures it. 

From the points A and B as 
centres, describe with the same 
radius two arcs cutting each other 
in D: through D and the centre 
C draw CD: the angle ACE will 
be equal to the angle ECB, and 
the arc AE to the arc EB. 


and AEB the arc which 


c 



V, Through a given point to draw a parallel to a given line. 

52. Let A be the given point, and BC the given line. 

3 









34 


ELEMENTS OF SURVEYING. 


[BOOK 1 


From 4 as a centre, with a 
radius greater tlian the shortest 
distance from A to DO, describe 
the indefinite arc ED: from the 
poiut E as a centre, with the same radius, describe the 
arc AF; make ED = AF, and draw AD: then will AD 
be the parallel required. 



YI. Two angles of a triangle being given , to find the third 


53. Draw the indefinite line 
DEF. At the point E, make 
the angle DEO equal to one of 
the given angles, and the angle 
OEH equal to the other: the re¬ 
maining angle HEF will be the D 
third angle required. 



VII. To represent , on paper , a line of a given length , so that 
any number of its parts shall correspond to the unit of the 
scale. 

54. Suppose that the given line were 75 feet in length, 
and it were required to draw it on paper, on a scale of 25 
feet to the inch. 

The length of the line 75 feet, being divided by 25, 
will give 3, the number of inches which will represent the 
line on paper. 

Therefore, draw the indefinite line AB, on which lay 


off a distance AC equal to 3 inches: A0 will represent 
the given line of 75 feet, drawn on the required scale. 

Remark I. This problem explains the manner of repre 
senting a line upon paper, so that a given number of its 
parts shall correspond to the unit of the scale, whether 
that unit be an inch or any part of an inch. 

When the length of the line to be laid down is given, 
and it has been determined how many parts of it are to 






SEC. II.] GEOMETRICAL CONSTRUCTIONS 


35 


be represented on the paper by a distance equal to the 
unit of the scale, we find the length which is to be taken 
from the scale by the following 

RULE. 

Divide the length of the line by the number of parts which 
is to be represented by the unit of the scale: the quotient will 
show the number of units which is to be taken from the scale . 

EXAMPLES. 

1. If a line of 640 feet is to be laid down on paper, on 
a scale of 40 feet to the inch; what length must be taken 
from the scale ? 

40)640(16 inches. 

2. If a line of 357 feet is to be laid down on a scale 
of 68 feet to the unit of the scale, (which we will suppose 
half an inch), how many parts are to be taken? 

a„. J 5.25 parts, or 
' (2.625 inches. 

3. A line of 384 feet is drawn on paper, on a scale of 
45 feet to the inch; what is its length on the paper? 

Ans. 8.53 inches. 

Remark II. When the length of a line on the paper is 
given, and it is required to find the true length of the 
line which it represents, take the line in the dividers and 
apply it to the scale, and note the number of units, and 
parts of a unit to which it is equal. Then multiply this 
number by the number of parts which the unit of the 
scale represents, and the product will be the length of the 
line. 

For example, suppose the length of a line drawn on 
the paper was found to be 3.55 inches, the scale being 40 
feet to the inch: then, 

3.55 X 40 = 142 feet, the length of the line. 


86 


ELEMENTS OF SURVEYING. 


[BOOK I. 


Y r IIL Having given two sides and the included angle of a tri¬ 
angle , to describe the triangle. 

55. Let tlie line L> = 150 feet, and 0 = 120 feet, be the 
given sides; and A = 80 degrees, the given angle: to de¬ 
scribe the triangle on a scale of 200 feet to the inch. 

Draw the indefinite line B G , and 
at the point D , make the angle GBH 
equal to 80 degrees: then lay off 
DG equal to 150, equal to three 
quarters of an inch, and DH equal 
to 120, equal to six tenths of an 

inch, and draw GII: BHG will be the required triangle. 



IX. The three sides of a triangle being given , to describe the 

triangle. 

56. Let A , B and (7, be the sides. 

Draw BE equal to the side A. 

From the point B as a centre, with 
a radius equal to the second side B , 
describe an arc: from E as a cen¬ 
tre, with a radius equal to the third 
side 0, describe another arc inter¬ 
secting the former in F; draw BF and EF\ and BFE will 
be the triangle required. 



By 

6U 


X. Having given two sides of a triangle and an angle oppo¬ 
site one of them , to describe the triangle. 

57. Let A and B be the given sides, and O the given 
angle, which we will suppose is opposite the side B. 

Draw the indefinite line BF 
and make the angle FBH equal to 
the angle C: take BH=A , from 
the point H, as a centre, with a 
radius equal to the other given 
side, B , describe an arc cutting 
BF in F; draw HF: then will BHF be the required tri¬ 
angle. 















8E0. II.] GEOMETRICAL CONSTRUCTIONS 


87 



E 


If the angle C is acute, and A>- 
the side B less than A, then B\ 
the arc described from the 
centre E with the radius EF 
— B will cut the side BE in 
two points, F and G, lying on 
the same side of D: hence, there will be two triangles, 
DEF ) and DEG , either of which will satisfy all the condi¬ 
tions of the problem. 



XI. The adjacent sides of a parallelogram , with the angle 
which they contain, being given , to describe the paral¬ 
lelogram. 

58. Let A and B be the given sides, and 0 the given 
angle. 

Draw the line Dll , and 
lay off DE equal to A ; at 
the point D , make the angle 
EDF= 0; take DF—B: de¬ 
scribe two arcs, the one from 
F\ as a centre, with a radius EG = DE, the other from E, as 
a centre, with a radius EG = DF; through the point G, 
where these arcs intersect each other, draw FG , EG ; DEGF 
will be the parallelogram required. 

XII. To find the centre of a given circle or arc . 

59. Take three points, A, B , 0\ any where in the cir 
cumference, or in the arc: 
draw AB, BO; bisect these two 
lines by the perpendiculars, DE, 

FG: the point 0 , where these 
perpendiculars meet, will be the 
centre sought. 

The same construction serves 
for making a circumference pass 
through three given points A , B, 

C\ and also for describing a circumference, about a given 
triangle. 


















SB 


ELEMENTS OF SURVEYING. 


[BOOK L 


PLANE TRIGONOMETRY. 


SECTION III. 

DEFINITIONS.—APPLICATION TO HEIGHTS AND DISTANCES. 


1. In every plane triangle there are six parts: three 
sides and three angles. These parts are so related to each 
other, that when one side and any two other parts are 
given, the remaining ones can be obtained, either by geo¬ 
metrical construction or by trigonometrical computation. 

2. Plane Trigonometry explains the methods of com¬ 
puting the unknown parts of a plane triangle, when a suf¬ 
ficient number of the six parts is given. 

3. For the purpose of trigonometrical calculation, the 
circumference of the circle is supposed to be divided into 
360 equal parts, called degrees; each degree is supposed 
to be divided into 60 equal parts, called minutes; and 
each minute into 60 equal parts, called seconds. 

Degrees, minutes, and seconds, are designated respec¬ 
tively, by the characters ° ' For example, ten degrees , 
eighteen minutes, and fourteen seconds , would be written 
10° 18' 14". 

4. If two lines be drawn through the centre of the 
circle, at right angles to each other, they will divide the 
circumference into four equal parts, of 90° each. Every 
right angle then, as EOA, is measured by an arc of 90°; 
every acute angle, as BOA, by an arc less than 90°; and 
every obtuse angle, as FOA, by an arc greater than 90°. 

5. The complement of an arc is • L o 


what remains after subtracting the 
arc from 90°. Thus, the arc EB 
is the complement of AB. The 
sum of an arc and its complement 
is equal to 90°. 


6. The supplement of an arc is 
what remains after subtracting the 
arc from 180°. Thus, GF is the 



a 













PLANE TRIGONOMETRY 


S E C. L] 


39 


supplement of tlie arc AEF. The sum of an arc and its 
supplement is equal to 180°. 

7. The sine of an arc is the perpendicular let fall from 
one extremity of the arc on the diameter which passes 
through the other extremity. Thus, BE is the sine of the 
arc AB. 

8. The cosine of an arc is the part of the diameter in¬ 
tercepted between the foot of the sine and centre. Thus, 
OD is the cosine of the arc AB. 


9. The tangent of an arc is the line which touches it at 
one extremity, and is limited by a line drawn through the 
other extremity and the centre of the circle. Thus, A 0 is 
the tangent of the arc AB. 

10. The secant of an arc is the line drawn from the 
centre of the circle through one extremity of the arc, and 
limited by the tangent passing through the other extremi¬ 
ty. Thus, 00 is the secant of the arc AB. 

11. The four lines, BD, OD, AC, OC, depend for their 
values on the arc AB and the radius OA; they are thus 
designated: 

sin AB for BD 
cos AB for OD 
tan AB for AO 
sec AB for 00 

12. If ABB be equal to a quadrant, or 90°, then EB 
will be the complement of AB. Let the lines ET and IB 
be drawn perpendicular to OE. Then, 

ET 1 , the tangent of EB, is called the cotangent of AB; 

IB, the sine of EB, is equal to the cosine of AB; 

OT, the secant of EB, is called the cosecant of AB, 

In general, if A is any arc or angle, we have, 

cos A = sin (90° — ^1) 
cot A — tan (90° — A) 
cosec A = sec (90° — A) 


i 


40 


ELEMENTS OF SURVEYING. 


[BOOR J 


13. If we take an arc, ABEF\ 
greater than 90°, its sine will be 
FH ; Oil will be its cosine ; A Q 
its tangent, and OQ its secant. 

"But FH is the sine of the arc GI\ 
which is the supplement of AF, 
and OH is its cosine; hence, the 
sine of an arc is equal to the sine of 
its supplement ; and the cosine of an 
arc is equal to the cosine of its supplementA 

Furthermore, AQ is the tangent of the arc AF\ and 
OQ is its secant: GL is the tangent, and OL the secant 
of the supplemental arc GF. But since AQ is equal to 
GL , and OQ to OL, it follows that, the tangent of an arc 
is equal to the tangent of its supplement; and the secant of an 
arc is equal to the secant of its supplementA 

TABLE OF NATURAL SINES. 

14. Let us suppose, that in a circle of a given radius, 
the lengths of the sine, cosine, tangent, and cotangent, have 
been calculated for every minute or second of the quad¬ 
rant, and arranged in a table; such a table is called a 
table of sines and tangents. If the radius of the circle is 
1, the table is called a table of natural sines. A table of 
natural sines, therefore, shows the values of the sines, co¬ 
sines, tangents, and cotangents of all the arcs of a quad¬ 
rant, which is divided to minutes or seconds. 

If the sines, cosines, tangents, and secants are known 
for arcs less than 90°, those for arcs which are greater can 
be found from them. For if an arc is less than 90°, its 
supplement will be greater than 90°, and the numerical 
values of these lines are the same for an arc and its sup¬ 
plement. Thus, if we know the sine of 20°, we also know 
the sine of its supplement 160°; for the two are equal to 
each other. The Table of Natural Sines, beginning at page 
63, of the tables shows the values of the sines and cosines 
only. 



* These relations are between the numerical values of the trigonometrical lines; 
the algebraic signs, which they have in the different quadrants, are not considered. 













SEC. III.] 


PLANE TRIGONOMETRY. 


41 


TABLE OP LOGARITHMIC SINES. 

15. In this table are arranged the logarithms of the 
numerical values of the sines, cosines, tangents, and co¬ 
tangents of all the arcs of a quadrant, calculated to a ra¬ 
dius of 10,000,000,000. The logarithm of this radius is 10. 
In the first and last horizontal lines of each page, are writ¬ 
ten the degrees whose sines, cosines, &c., are expressed on 
the page. The vertical columns on the left and right, are 
columns of minutes. 


CASE I. 

To find, in the table , the logarithmic sine, cosine, tangent , or 
cotangent of any given arc or angle. 

1G. If the angle is less than 45°, look for the degrees 
in the first horizontal line of the different pages: when the 
degrees are found, descend along the column of minutes, on 
the left of the page, till you reach the number showing the 
minutes : then pass along a horizontal line till you come into 
the column designated, sine, cosine, tangent, or cotangent, as 
the case may be: the number so indicated is the logarithm 
sought. Thus, on page 37, for 19° 55', we find, 

sine 19° 55 # ... . 9.532312 

cos 19° 55' .... 9.973215 

tan 19° 55' ... . 9.559097 

cot 19° 55' ... . 10.440903 

17. If the angle is greater than 45°, search for the de¬ 
grees along the bottom line of the different pages : when the 
number is found, ascend along the column of minutes on the 
right hand side of the page, till you reach the number express¬ 
ing the minutes: then pass along a horizontal line into the 
column designated tang, cot, sine, or cosine, as the case may 
be: the number so pointed out is the logarithm required. 

18. The' column designated sine, at the top of the page, 
is designated by cosine at the bottom; the one designated 
tang, by cotang, and the one designated cotang, by tang. 

The angle found by taking the degrees at the top of 
the page, and the minutes from the left hand vertical column, 
is the complement of the angle found by taking the degrees 


42 


ELEMENTS OF SURVEYING. 


[BOOK L 


at tlie bottom of the page, and tbe minutes from tbe right 
hand column on the same horizontal line with the first. 
Therefore, sine, at the top of the page, should correspond 
with cosine, at the bottom; cosine with sine, tang with 
cotang, and cotang with tang, as in the tables (Art. 12). 

If the angle is greater than 90°, we have only to sub¬ 
tract it from 180°, and take the sine, cosine, tangent, or 
cotangent of the remainder. 

The column of the table next to the column of sines, 
and on the right of it, is designated by the letter D . 
This column is calculated in the following manner. 

Opening the table at any page, as 42, the sine of 24° 
is found to be 9.609313; that of 24° 01', 9.609597: their 
difference is 284; this being divided by 60, the number 
of seconds in a minute, gives 4.73, which is entered in the 
column D. 

Now, supposing the increase of the logarithmic sine to 
be proportional to the increase of the arc, and it is nearly 
so for 60", it follows, that 4.73 is the increase of the sine 
for 1". Similarly, if the arc were 24° 20', the increase of 
the sine for 1", would be 4.65. 

The same remarks are applicable in respect of the 
column D ) after the column cosine, and of the column D. 
between the tangents and cotangents. The column D , be¬ 
tween the columns tangents and cotangents, answers to 
both of these columns. 

Now, if it were required to find the logarithmic sine 
of an arc expressed in degrees, minutes, and seconds, we 
have only to find the degrees and minutes as before; then, 
multiply the corresponding tabular difference by the sec¬ 
onds, and add the product to the number first found, foi 
the sine of the given arc. 

Thus, if we wish the sine of 40° 26' 28". 

The sine 40° 26' ... 9.811952 

Tabular difference 2.47 . 

Number of seconds 28 . 

Product, 69.16 to be added 69.18 

Gives for the sine of 40° 26' 28". 


9.812021. 





SEC. Ill] 


PLANE TRIGONOMETRY. 


43 


Tlie decimal figures at the right are generally omitted 
in the last result; hut when they exceed five-tenths, the 
figure on the left of the decimal point is increased by 1; 
the logarithm obtained is then exact, to within less than 
one unit of its right hand place. 

The tangent of an arc, in which there are seconds, is 
found in a manner entirely similar. In regard to the co¬ 
sine and cotangent, it must be remembered, that they in¬ 
crease while the arcs decrease, and decrease as the arcs are 
increased; consequently, the proportional numbers found 
for the seconds, must be subtracted, not added. 

EXAMPLES. 

1. To find the cosine of 3° 40' 40". 

The cosine of 3° 40' . . 9.999110 

Tabular difference .13 . 

Number of seconds 40 

Product, 5.20 to be subtracted 5.20 

Gives for the cosine of 3° 40' 40" 9.999105. 

2. Find the tangent of 37° 28' 31". 

Ans. 9.884592. 

3. Find the cotangent of 87° 57' 59". 

Ans. 8.550356. 


CASE II. 

To find the degrees, minutes , and seconds answering to any 
given bgarithmic sine, cosine, tangent, or cotangent. 

19. Search in the table, in the proper column, and 
if the number is found, the degrees will be shown either 
at the top or bottom of the page, and the minutes in the 
side column either at the left or right. 

But, if the number cannot be found in the table, take 
from the table the degrees and minutes answering to the 
nearest less logarithm, the logarithm itself, and also the 
corresponding tabular difference. Subtract the logarithm 
taken from the table from the given logarithm, annex two 





44 


ELEMENTS OF SURVEYING. 


[BOOK 1 


ciphers to the remainder, and then divide the remainder 
by the tabular difference: the quotient will be seconds, 
and is to be connected with the degrees and minutes be¬ 
fore found: to be added for the sine and tangent, and 
subtracted for the cosine and cotangent. 


EXAMPLES. 

1. Find the arc answering to the sine 9.880054 
Sine 49° 20, next less in the table 9.879963 

Tabular difference, 1.81)91.00(50 / . 

Hence, the arc 49° 20' 50" corresponds to the given sine 
9.880054. 

2. Find the arc whose cotangent is 10.008688 
cot 44° 26', next less in the table 10.008591 

Tabular difference, 4.21)97.00(23". 

Hence, 44° 26' — 23" = 44° 25' 37" is the arc answering 
to the given cotangent 10.008688. 

3. Find the arc answering to tangent 9.979110. 

Ans. 43° 37' 21". 

4. Find the arc answering to cosine 9.944599. 

Ans. 28° 19' 45". 

20. IVe shall now demonstrate the principal theorems 
of Plane Trigonometry. 

THEOREM I. 


The sides of a plane triangle are proportional to the sines of 

their opposite angles. 

21. Let ABC be a triangle; then will 

CB : CA : : sin A : sin B. 


For, with A as a centre, and AD 
equal to the less side BC, as a ra¬ 
dius, describe the arc DI: and with 
B as a centre and the equal radius 
BO y describe the arc CL , and draw 


c 



DE and CF perpen¬ 


dicular to AB: now DE is the sine of the angle H, and 








SEC. Ill] PLANE TRIGONOMETRY. 45 

CF is the sine of B, to the same radius AD or BC. But 
by similar triangles, 

AD \ DE : : AC : CF. 

But AD being equal to BC, we have 

BC : sin A : : AC : sin B, or 

BC : AC : : sin A : sin B. 

By comparing the sides AB\ AC, in a similar manner, 
we should find, 

AB : AC ‘ : sin C : sin B. 

THEOREM II. 

In any triangle, the sum of the two sides containing either 
angle, is to their difference, as the tangent of half the sum of 
the two other angles, to the tangent of half their difference. 

22. Let ACB be a triangle: then will 
AB+AC : AB—AC :: tan l(C+B) : tan \{C—B). 

With i as a centre, and a E 

radius AC, the less of the two 
given sides, let the semicircumfe- ! \ / 
rence IFCE be described, meeting \ \ • / \\7 

AB in I, an d^BA produced, in E. 

Then, L?^will be the sum of the C FGIT B 

sides, and BI their difference. Draw Cl and AF. 

Since CAE is an outward angle of the triangle ACB, 
it is equal to the sum of the inward angles C and B (Bk. 
I., Prop. XXV., Cor 6). But the angle CIE being at the 
circumference, is half the angle CAE at the centre (Bk. III., 
Prop. XVIII.); that is. half the sum of the angles C and 
B, or equal to \(C-\-B). 

The angle AFC= ACB, is also equal to ABC+ BAF, 
therefore, BAF = A CB — ABC. 

But, ICF=l(BAF) = -l(ACB-ABC), or i(C-B). 

With / and C as centres, and the common radius IC, 
let the arcs CD and IC be described, and draw the lines 
CE and III perpendicular to IC. The perpendicular CE 
will pass through E, the extremity of the diameter 





» 


46 


ELEMENTS OF SURVEYING. [BOOK I 



since tlie right angle ICE must be 
inscribed in a semicircle. 

But CE is the tangent of CTE 
= |(6 , + ^); and IH is the tan¬ 
gent of ICB—\(C—B), to the 

common radius CI. C" ' . -- 'FGH 

But since the lines CE and IH are parallel, the tri¬ 
angles BET. and BCE are similar, and give the proportion, 

BE : BI : : CE : IH, or 

by placing for BE and BI, CE and IH, their values, we 
have 

AB + AC : AB—AC :: tan \{CAB) : tan \{C—B). 


THEOREM III. 

In any plane triangle, if a line is drawn from the vertical 
angle perpendicular to the base, dividing it into two segments: 
then, the whole base, or sum of the segments, is to the sum of 
the two other sides, as the difference of those sides to the differ¬ 
ence of the segments. 

23. Let BAC be a triangle, and AD perpendicular to the 
base; then will 

BC : CA + AB :: CA-AB : CD-DB. 

For, AB" = BD" + AD" 

(Bk. IV., Prop. XI.); 

and AO"~ = lXf + AD"~ 

-o -2 

by subtraction, A C~ — AB = 

CD 2 - BD 2 . 

But since the difference of 
the squares of two lines is equivalent to the rectangle con¬ 
tained by their sum and difference (Bk. IY., Pron. X.), we 
have, 

AC 2 - AB' = {AC+ AB ). (AC- AB) 

and OB" - DB' = (CD + DB).(CD-DB) 

therefore, (CD + DB).(CD-DB) = (AC+AB).(AC- AB) 
hence, CD+DB : AC+AB :: AC-AB : CD-DR 


A 





















SEC. Ill] 


PLANE TRIGONOMETRY. 


47 


THEOREM IV. 

In any right-angled plane triangle , radius is to the tangent 
of either of the acute angles , as the side adjacent to the side 
opposite. 

24. Let GAB be the proposed triangle, and denote the 
radius by R: tben will ^ 

R : tan G : : AG : AB. 

For, with any radius as GD de¬ 
scribe the arc DH, and draw the tan¬ 
gent DG. 

From the similar triangles GDG and GAB , we have, 

GD : DG : : GA : AB ; hence, 

R : tan Gw GA : AB. 

By describing an arc with 5 as a centre, we could 
show in the same manner that, 

R : tan B : : AB : AG. 



THEOREM V. 


In every right-angled plane triangle , radius is to the cosine 
of either of the acute angles , as the hypothenuse to the side 
adjacent. 


25. Let ABG be a triangle/right-angled at B: then will, 


R : cos A : : AG : AB. 

For, from the point A as a centre, 

■with any radius as AD , describe the 
arc DI\ which will measure the angle 
A, and draw DE perpendicular to AB: then will AE be 
the cosine of A. 

The triangles ADE and AGB , being similar, we have, 



AD : AE : : AG : AB: that is, 

R : cos A : : AG : AB. 


Kemark. The relations between the sides and angles 
of plane triangles, demonstrated in these five theorems, are 


I 







\ 


48 ELEMENTS OF SURVEYING. [BOOK I 

sufficient to solve all tlie cases of Plane Trigonometry. 
Of the six parts which make up a plane triangle, three 
must be given, and at least one of these a side, before the 
others can be determined. 

If the three angles only are given, it is plain, that an 
indefinite number of similar triangles may be constructed, 
the angles of which shall be respectively equal to the 
angles that are given, and therefore, the sides could not be 
determined. 

Assuming, with this restriction, any three parts of a 
triangle as given, one of the four following cases will al¬ 
ways be presented. 

I. When two angles and a side are given. 

II. When two sides and an opposite angle are given. 

III. When two sides and the included angle are given. 

IY. When the three sides are given. 

CASE I. 

When two angles and a side are given. 

26. Add the given angles together, and subtract their 
sum from 180 degrees. The remaining parts of the tri¬ 
angle can then be found by Theorem I. 

EXAMPLES. 

1. In a plane triangle, ABO, 
there are given the angle A = 58° 07', 
the angle B— 22° 87', and the side 
AB = 408 yards. Bequired the oth¬ 
er parts. 



GEOMETRICALLY. 

27. Draw an indefinite straight line, AB, and from the 
scale of equal parts lay off AB equal to 408. Then, 
at A, lay off an angle equal to 58° 07', and at B an angle 
equal to 22° 87', and draw the lines AO and BO: then 
will ABO be the triangle required. 

The angle 0 may be measured either with the protractor 
or the scale of chords (Sec. II., Arts. 42 and 44), and will be 



SEC III] 


PLANE TRIGONOMETRY. 


49 


found equal to 99° 16'. The sides AG and BC may be 
measured by referring them to the scale of equal parts 
(Sec. II., Art. 40). We shall find A G= 158.9 and BG — 851 
yards. 


TRIGONOMETRICALLY BY LOGARITHMS. 

To the angle ... A — 58° 07' 

Add the angle . . B = 22° 87' 

Their sum, = 80° 44' 

taken from . . . 180° 00' 

leaves G ... . 99° 16', of which, as it ex¬ 

ceeds 90°, we use the supplement 80° 44'. 


sin G 
: sin A 
: : AB 


To find the side BG. 


99° 16' ar. comp. 0.005705 
58° 07' ...... . 9.928972 

408 . 2.610660 


BG 851.024 (after rejecting 10) 2.545337. 


Remark. The logarithm of the fourth term of a pro¬ 
portion is obtained by adding the logarithm of the second 
term to that of the third, and subtracting from their sum 
the logarithm of the first term. But to subtract the first 
term is the same as to add its arithmetical complement 
and reject 10 from the sum (Sec. I., Art. 13): hence, the arith¬ 
metical complement of the first term added to the loga¬ 
rithms of the second and third terms, minus ten, will give 
the logarithm of the fourth term. 



To find the side A G. 


sin G 

99° 16' ar. comp. 

0.005705 

sin B 

22° 37'. 

9.584968 

AB 

(4^ 

O 

GO 

• 

• 

• 

• 

• 

2.610660 

AG 

158.976 . 

2.201333 


2. In a triangle ABC\ there are given A = 38 J 25’ 
Z?=57° 42', and AB — 400: required the remaining parts. 

Ans G=8 3° 53', Rtf=249.974, AG= 340.04. 

4 











50 


ELEMENTS OF SURVEYING. 


[BOOK 2 


CASE II. 

When two sides and an opposite angle are given. 


28. In a plane triangle, ABC\ 
there are given AC— 216, CB = 117, 
the angle A — 22° 87', to find the 
other parts. 


c 



GEOMETRICALLY. 

29. Draw an indefinite right line ABB' : from any 
point, as A , draw AG\ making BAC =22° 37', and make’ 
A (7= 216. With C as a centre, and a radius equal to 117, 
the other given side, describe the arc B'B\ draw B'C and 
BC: then will either of the triangles ABC or AB'C } an¬ 
swer all the conditions of the question. 

TRIGONOMETRICALLY. 


To find the angle B. 


BC 
AC 
sin A 

117 
216 . 
22° 37' . 

ar. comp. 

7.931814 

2.334454 

9.584968 

sin B' 

45° 13' 55", 

or ABO 184° 46' 05'' 

9.851236- 


The ambiguity in this, and similar examples, arises in 
consequence of the first proportion being true for either 
of the angles ABC, or AB C ) which are supplements of 
each other, and therefore, have the same sine (Art. 18). 
As long as the two triangles exist, the ambiguity will con¬ 
tinue. But if the side CB, opposite the given angle, is 
greater than A C, the arc BB will cut the line ABB, on 
the same side of the point A, in but one point, and then 
there will be only one triangle answering the conditions. 

If the side CB is equal to the perpendicular Cd } the 
arc BB' will be tangent to ABB, and in this case also 
there will be but one triangle. When CB is less than the 
perpendicular Cd , the arc BB will not intersect the base 
ABB , and in that case, no triangle can be formed, or it 
will be impossible to fulfil the conditions of the problem. 








SEC. Ill] 


PLANE TRIGONOMETRY. 


51 


2. Given two sides of a triangle 50 and 40 respectively 
and the angle opposite the latter equal to 32°: required 
the remaining parts of the triangle. 

Ans. If the angle opposite the side 50 is acute, it is 
equal to 41° 28' 59"; the third angle is then equal to 
106° 81' 01", and the third side to 72.368. If the angle 
opposite the side 50 is obtuse, it is equal to 138° 31' 01 /: , 
the third angle to 9° 28' 59", and the remaining side to 
12.436. 


CASE III. 


When the two sides and their included angle are given . 


30. Let ABO be a triangle; AB , 
BO ) the given sides, and B the 
given angle. 

Since B is known, we can find 
the sum of the two other angles: 
for 


A. 



A + C— 180° — B, and, 
+ (7) = K1S0° - 


We next find half the difference of the angles A and 
C by Theorem II., viz., 

BO A BA : BQ-BA :: tan\(AAO) : tan 

in which we consider BO greater than BA , and therefore 
A is greater than (7; since the greater angle must be op¬ 
posite the greater side. 

Having found half the difference of A and C, by add¬ 
ing it to the half sum, \{A + (7), we obtain the greater 
angle, and by subtracting it from half the sum, we obtain 
the less. That is, 

\{A AO) A i(A — 0) = A, and 
■1-{A AO)- \(A -0)=0. 

Having found the angles A and (7, the third side AC 
may be found by the proportion, 

sin A : sin B : : BO : AC, 



52 


ELEMENTS OF SURVEYING. 


[BOOK I 


EXAMPLES. 

1. In the triangle ABC\ let 1267=540, AB = 450, and 
the included angle B — 80°: required the remaining parts. 

GEOMETRICALLY. 

31. Draw an indefinite right line BC\ and from any 
point, as B } lay olf a distance 1267=540. At B make the 
angle CBA = 80° : draw BA , and make the distance 
BA — 450; draw A 67; then will ABC be the required tri¬ 
angle. 


TRIGONOMETRICALLY. 

BC+BA = 540 + 450 = 990; and BC-BA = 540 - 450 = 90. 

A + C= 180° — B= 180° - 80° = 100°, and therefore, 
\{A + 67) = J(100°) = 50°. 


To find -J(A — 67). 

BCABA 990 ar. comp. 7.004365 

BC - BA 90 . 1.954243 

: tan \{A + 67) 50°. 10.076187 

tan - 67) 6° IV . 9.034795. 


Hence, 50° + 6° 11'= 56° 11' = A; and 50°-6° 11' = 

43° 49' = 67. 

» - 

To find the third side AC. 


sin 67 43° 49' ar comp. 0.159672 

sin B 80° . 9.993351 

: AB 450 . 2.653213 


A 67 640.082 . 2.806236. 


2 Given two sides of a plane triangle, 1686 and 960, 
and their included angle 128° 04': required the other parts. 
Ans. Angles, 33° 34' 39"; 18° 21' 21"; side 2400. 

CASE IV. 

32. Having given the three sides of a plane triangle, 
to find the angles. 














SEC. III.] 


PLANE TRIGONOMETRY. 


53 


Let fall a perpendicular from the angle opposite the 
greater side, dividing the given triangle into two right- 
angled triangles • then find the difference of the segments 
of the base by Theorem III. Half this difference being 
added to half the base, gives the greater segment; and, 
being subtracted from half the base, gives the less segment. 
Then, since the greater segment belongs to the right-angled 
triangle having the greater hypothenuse, we have two 
sides and the right angle of each of two right-angled tri¬ 
angles, to find the acute angles. 


EXAMPLES. 


1. The sides of a plane triangle 
being given ; viz., BC— 40, A C= 34, 
and AB — 25 : required the angles. 



GEOMETRICALLY. 

33. With the three given lines as sides construct a tri¬ 
angle as in Prob. IX. Then measure the angles of the 
triangle either with the protractor or scale of chords. 

TRIGONOMETRICALLY. 

BC : AC+AB :: AC-AB : CD-BD , 

That is, 40 : 59 : : 9 : = 13.275. 

40 

Then, 40 + 13.2/5 = 2 6.6375 = CD, 

A 

And, ~ ° -13.275 = 13 -3625 = BD 

A 

In the triangle BAG\ to find the angle BAG. 


AC 34 ar. comp. 8.468521 

: BC 26.6375 . 1.425493 

:: sin B 90° . 10.000000 


: sin BAG 51° 34'40". 9.894014, 











54 


ELEMENTS OF SURVEYING. [BOOK I 


In the triangle BAD , to find the angle BAD. 


AB 25 ar. comp. 8.602060 

BD 13.3625 1.125887 

• sin D 90°. 10.000000 

sin BAD 32° 18' 35". 9.727947. 


Hence, 90° - DAO= 90° - 51° 34' 40" = 38° 25' 20" == G\ 
and, 90° - BAD = 90° - 32° 18' 35" = 57° 41' 25" «= B, 
and, BAD + DAG == 51° 34' 40" + 32° 18' 35" = 83° 53' 

15" = A. 

2. In a triangle, of which the sides are 4, 5, and 6, 
what are the angles ? 

Arts. 41° 24' 35"; 55° 46' 16"; and 82° 49' 09". 


SOLUTION OF RIGHT-ANGLED TRIANGLES. 

34. The unknown parts of a right-angled triangle may 
be found by either of the four last cases; or, if two of the 
sides are given, by means of the property that the square 
of the hypothenuse is equivalent to the sum of the squares 
of the two other sides. Or the parts may be found by 
Theorems IY. and Y. 


EXAMPLES. 


1. In a right-angled triangle 
BAO, there are given the hypothe¬ 
nuse BO =250 , and the base AC= 
240: required the other parts. 




To find the angle B. 


BO 

250 ar. comp. 

7.602060 

AO 

240 . 


: sin A 

90°. 


sin B 

73° 44'28" .... 

. . 9.982271. 


But (7= 90° - B= 90° — 73° 44' 23" = 16° 15' 37": 
















SEC. III.J PLANE TRIGONOMETRY. 66 

Or C may be found from the proportion. 

OB 360 ar. comp. 7.602060 

AC 240 . 2.380211 

:: It . 10.000000 

: cos C 16° 15' 37". 9.982271. 


To find side AB by Theorem IV. 

It ar. comp. 0.000000 

. tan O 16° 16' 37" . .. 9.464889 

:: AC 240 2.380211 

AB 70.0003 . 1.846100. 


2. In a right-angled triangle BAG, there are given 
AC = 384, and B— 63° 08': required the remaining parts. 

Ans. AB = 287M; £(7=479.979; C= 36° 62'. 

« 

APPLICATION TO HEIGHTS AND DISTANCES. 

L To determine the horizontal distance to a point which is in¬ 
accessible by reason of an intervening river* 

35. Let C be the point. Measure 
along tlie bank of tbe river a hori* 
zontal base line AB, and select tbe 
stations A and B, in sucb a man¬ 
ner that eacb can be seen from tbe 
other, and tbe point 0 from botb 
of them. Then measure tbe hori¬ 
zontal angles CAB and CBA, with 
an instrument adapted to that purpose. 

Let us suppose that we have found AB = 600 yards, 
CA B = 57° 35', and CBA = 64° 51'. 

Tbe angle C — 180° — (A + B) = 57° 34'. 

To find the distance BC. 


sin C 57° 34' ar. comp. 0.073649 

sin A 57° 35'. 9.926431 

: AB 600 . 2.778151 

BC 600.11 yards. 2.778231. 



* Kead definitions, from 3 to 14, pages 64 and 65. 




































56 


ELEMENTS OF SURVEYING. 


[BOOK I 


To find the distance AC. 


sin C 57° 34' ar. comp. 0.073649 

. sin B 64° 51'. 9.956744 

:: AB 600 . 2.778151 

: AC 643.94 yards. 2.808544, 


IL To determine the altitude of an inaccessible object above a 

given horizontal plane. 


FIRST METHOD. 



36. Suppose B to be tlie inac¬ 
cessible object, and BC the hori¬ 
zontal plane from which the alti¬ 
tude is to be estimated: then, if 
we suppose BC to be a vertical 
line, it will represent the required 
distance. 

Measure any horizontal base line, as BA ; and at the 
extremities B and A , measure the horizontal angles CBA 
and CAB. Measure also the angle of elevation BBC. 

Then in the triangle CBA there will be known, two 
angles and the side AB ; the side BO can therefore be 
determined. Having found BC\ we shall have, in the 
right-angled triangle BBC\ the base BC and the angle at 
the base, to find the perpendicular BC\ which measures 
the altitude of the point B above the horizontal plane BC. 

Let us suppose that we have found 


IL4 = 780 yards, the horizontal angle CBA — 41° 24'; 
the horizontal angle CAB— 96° 28', and the angle of eleva¬ 
tion 2*50= 10°43'. 

In the triangle BCA , to find the horizontal distance BC 
The angle BCA = 180° - (41° 24' + 96° 28') = 42° 08' = C. 


sin C 42° 08' ar. comp. 0.173369 

sin A 96° 28'. 9.997228 

: AB 780 2.892095 

BC 1155.29 . 3.062692. 















SEC. Ill] 


PLANE TRIGONOMETRY. 


57 


In the right-angled triangle DBC , to find DC. 


R ar. comp. 0.000000 

tan DBC 10° 43'. 9.277043 

BC 1155.29 ....... 3.062692 

DC 218.64 ....... 2.339735. 


Remark I. It might, at first, appear, that the solution 
which we have given, requires that the points B and A 
should be in the same horizontal plane; but it is entirely 
independent of such a supposition. 

For, the horizontal distance, which is represented by 
BA , is the same, whether the station A is on the same 
level with J5, above it, or below it. The horizontal angles 
CAB and CBA are also the same, so long as the point C 
is in the vertical line DC. Therefore, if the horizontal 
line through A should cut the vertical line DC\ at any 
point, as E\ above or below C, AB would still be the hori¬ 
zontal distance between B and A , and AE\ which is equal 
to A C.\ v r ould be the horizontal distance between A and C. 

If at A, we measure the angle of elevation of the point 
D , we shall know in the right-angled triangle DAE ) the 
base AE\ and the angle at the base; from which the per¬ 
pendicular DE can be determined. 

37. Let us suppose that we had measured the angle of 
elevation DAE\ and found it equal to 20° 15'. 

First: In the triangle BAC\ to find AC or its equal AE. 


sin C 42° 08- ar. comp. 0.173369 

sin B 41° 24'.. 9.820406 

: AB 780 '. 2.892095 

AC 768.9 .. 2.885870. 


In the right-angled triangle DAE\ to find DE. 

R ar. comp. 0.000000 

tan A 20° 15'. 9.566932 

: AE 768.9 . 2.885870 

DE 283.66 . 2.452802. 




















58 ELEMENTS OF SURVEYING. [BOOK L 

» 

Now, since BC is less than 
BE, it follows that the station B 
is above the station A. That is, 

BE-BO— 283.66 - 218.64 = 

65.02 = EC, 

which expresses the vertical dis¬ 
tance that the station B is above 
the station A. 

Remark II. It should be remembered, that the vertical 
distance which is obtained by the calculation, is estimated 
from a horizontal line passing through the eye at the time 
of observation. Hence, the height of the instrument is to 
be added, in order to obtain the true result. 


D 



SECOND METHOD. 


38. When the nature of the ground will admit of it, 
measure a base line AB in the direction of the object B. 
Then measure with the instrument the angles of elevation 
at A and B. 

Then, since the out¬ 
ward angle BBC is 
equal to the sum of 
the angles A and ABB , 
it follows that the an¬ 
gle ABB is equal to the difference of the angles of eleva¬ 
tion at A and B. Hence, we can find all the parts of the 
triangle ABB. Having found BB ) and knowing the angle 
BBC, we can find the altitude BC. 

This method supposes that the stations A and B are on 
the same horizontal plane; and therefore it can only be 
used when the line AB is nearly horizontal. 

Let us suppose that we have measured the base line, 
and the two angles of elevation, and 



found 


■< 


AB 

A 

BBC- 


975 yards, 
15° 36', 

27° 29'; 


required the altitude BC. 








8EC. IIL] 


PLANE TRIGONOMETRY. 


59 


First: ADB- DBG - A = 27° 29' -15° 36' = 11° 53'. 
In the triangle ADB\ to find BD. 


sin D 11° 53' ar. comp. 0.686302 

: sin A 15° 36'. 9.429623 

: . AB 975 . 2.989005 

DB 1273.3 . 3.104930. 


In the triangle DBG\ to find DC. 


R ar. comp. 0.000000 

. sin B 27° 29'. 9.664163 

: : DB 1273.3 3.104930 

: DC 587.61 2.769093. 


III. To determine the perpendicular distance of an object below 

a given horizontal plane. 

39. Suppose C to be directly 
over the given object, and A the 
point through which the horizon¬ 
tal plane is supposed to pass. 

Measure a horizontal base line 
AB, and at the stations A and 
B conceive the two horizontal 
lines AC, BC, to be drawn. The 
oblique lines from A and B to the object are the hy- 
pothenuses of two right-angled triangles, of which AC,\ BO ' 
are the bases. The perpendiculars of these triangles are 
the distances from the horizontal lines AC\ BC\ to the 
object. If we turn the triangles about their bases AC, 
BC, until they become horizontal, the object, in the first 
case, will fall at C', and in the second at C". 

Measure the horizontal angles CAB, CBA, and also the 
angles of depression C'A C, C"BC. 

















60 


[BOOK I. 


ELEMENTS OF SURVEYING. 


Let us suppose that we have 


r 


found - 


AB = 672 yards 
BAC =72° 29' 
ABC = 39° 20 


C'AC — 27° 49' 
^G"BO= 19° 10'. 


First: in the triangle 

the horizontal angle A CB = 180° ~(-4 + jB) = 180 :> - 111 0 
49' = 68° 11'. 


To find the horizontal distance A C. 

sin C 68° 11' ar. comp. 0.032275 

sin B 39° 20 . 9.801973 

: AB 672 2.827369 

AC 458.79 2.661617 


To find the horizontal distance BC. 

sin C 68° 11' ar. comp. 0.032275 

sin A 72° 29'. 9.979380 

AB 672 2.827369 

BC 690.28 2^839024. 


In the triangle CAC\ to find CC'. 

R ar. comp. 0.000000 

: tan C’AC 27° 49'. 9.722315 

.: AC 458.79 . 2.661617 

: CC' 242.06 . .. 2.383932. 


In the triangle CBC ", to find CC". 

R ar. comp. 0.000000 

. tan C"BC 19° 10 . 9.541061 

: : BC 690.28 . 2.839024 

: CC" 239.93 . 2.380085. 

Hence also, CC - CC" = 242.06 - 239.93 = 2.13 yards, 


< 

which is the height of the station A above station B. 



























SEC. III.J 


PUNE TRIGONOMETRY. 


61 


PROBLEMS. 


1. Wanting to know the distance between two inacces¬ 
sible objects, which lie in a direct level line from the bot¬ 
tom of a tower of 120 feet in height, the angles of depres¬ 
sion axe measured from the top of the tower, and are found 
to be, of the nearer 57°, of the more remote 25° 30': re¬ 
quired the distance between the objects. 

2. In order to find the distance 
between two trees, A and B ) which 
could not be directly measured be¬ 
cause of a pool which occupied the 
intermediate space, the distances 
of a third point C from each of 
them were measured, and also the 
included angle ACB: it was found that, 

CB =672 yards, 

CA =588 yards, 

ACB — 55° 40'; 

required the distance AB. Arts. 592.967 yards. 

3. Being on a horizontal plane, and wanting to ascer¬ 
tain the height of a tower, standing on the top of an in¬ 
accessible hill, there were measured, the angle of elevation 
of the top of the hill 40°, and of the top of the tower 51°; 
then measuring in a direct line 180 feet farther from the 
hill, the angle of elevation of the top of the tower was 
33° 45'; required the height of the tower. 

Arts. 83.998. 


Ans. 173.656 feet. 



4. Wanting to know the hori¬ 
zontal distance between two inac¬ 
cessible objects E and W] the fol¬ 
lowing measurements were made. 


viz. 


AB =536 yards 
BA W = 40° 16' 

. WAE= 57° 40 
ABE = 42° 22' 


lEBW= 71° 07'; 
required the distance EW. 



Ans. 939.634 yards. 






















62 


ELEMENTS OF SURVEYING. 


[BOOK 1 


5. Wanting to know the 
horizontal distance between 
two inacessible objects A 
and i>. and not finding any 
station from which both of 
them could be seen, two 
points G and D, were chosen 
at a distance from each other, equal to 200 yards; from 
the former of these points A could be seen, and from the 
latter B , and at each of the points C and D a staff was 
set up. From G a distance GF was measured, not in the 
direction DC\ equal to 200 yards, and from D a distance 
DE equal to 200 yards, and the following angles taken, 

f AFG = 83° 00', BDE = 54° 30', 
viz. \ A CD = 53° 30', BDG = 156° 25', 

[ACF = 54° 31', BED = 88° 80'. 

Ans. AB=34t5A67 yards 



C 


6. From a station P there 
can be seen three objects, A , 

B and (7, whose distances from 
each other are known: viz., 

AB— 800, AC— 600, and BG 
— 400 yards. Now, there are 
measured the horizontal an¬ 
gles. 

APC=3S° 45' and BPG 
= 22° 30': it is required to 
find the three distances PA, PC\ and PB. 

PA = 710.193 yards. 
Ans. -! PC = 1042,522 
PB = 934.291. 



7. This problem is much used in maritime survey¬ 
ing, for the purpose of locating buoys and sounding boats. 
The trigonometrical solution is somewhat tedious, but it 
may be solved geometrically by the following easy con¬ 
struction. 






SEC. Ill] 


PLANE TRIGONOMETRY. 


63 


Let A , B, and 0 be the 
three fixed points on shore, 
and P the position of the 
boat from which the angles 
APC= 33° 45', CPB= 22° 30', 
and A PB=5Q° 15', have been 
measured. 

Subtract twice APO=67° 

30' from 180°, and lay off at 
A and 0 two angles, CA 0 , 

ACO , each equal to half the 
remainder = 56° 15'. With 
the point 0, thus determined, 
as a centre, and OA or 00 as a radius, describe the cir¬ 
cumference of a circle: then, any angle inscribed in the 
segment APC ) will be equal to 33° 45'. 

Subtract, in like manner, twice CPB—45°, from 180°, 
and lay off half the remainder = 67° 30', at B and C,\ de¬ 
termining the centre Q of a second circle, upon the cir¬ 
cumference of which the point P will be found. The 
required point P will be at the intersection of these two 
circumferences. If the point P fall on the circumference 
described through the three points A, B, and 0,\ the two 
auxiliary circles will coincide, and the problem will be in¬ 
determinate. 










BOOK II. 


PLANE SURVEYING 


SECTION I. 

DEFINITIONS.—MEASUREMENT OF ANGLES AND LINES. 

1. Surveying, in its most extensive signification, com¬ 
prises all the operations necessary for finding, 

1st. The area or contents of any portion of the surface 
of the earth; 

2d. The lengths and directions of the bounding lines; 
and, 

3d. For making accurate delineations of the surface and 
bounding lines on paper. 

It is divided into two branches, Plane and Geodesic 
Savveying. 

2. The radius of the earth being very large, the curva¬ 
ture may be neglected, when the survey is limited to small 
portions of the surface. This branch is called Plane Sur- 
veying. 

When the curvature is taken into account, as it must 
be in all extensive surveys, the method of measurement 
and computation is called Geodesic Surveying. 

3. If at any point of the surface of the earth, regarded 
as a sphere, a plane be passed perpendicular to the radius, 
it will be tangent to the surface. Such a plane, and all 
planes parallel to it, are called horizontal planes. 

4. A plane perpendicular to a horizontal plane, at a 
given point, is called a vertical plane. 



DEFINITIONS. 


65 


SEC. I.] 

5. All lines of horizontal planes are called horizontal 
lines. 

6. Lines which are perpendicular to a horizontal plane, 
are called vertical lines; and all lines which are inclined to 
it, are called oblique lines. 

Thus, AB and DC are hori¬ 
zontal lines; BC and AD are 
vertical lines ; and A C and BD 
are oblique lines. 

7. The horizontal distance 
between two points, is the horizontal line intercepted be¬ 
tween the two vertical lines passing through those points. 
Thus, D C or AB is the horizontal distance between the two 
points A and (7, or the points B and D. 

8. A horizontal angle is one whose sides are horizontal; 
its plane is also horizontal. 

A horizontal angle may also be defined to be, the angle 
included between two vertical planes passing through the angular 
point, and the two objects which subtend the angle. 

9. A vertical angle is one, the plane of whose sides is 
vertical. 

10. An angle of elevation , is a vertical angle having one 
of its sides horizontal, and the inclined side above the hor¬ 
izontal side. 

Thus, in the last figure, BAC is the angle of elevation 
from A to C. 

11. An angle of depression , is a vertical angle having 
one of its sides horizontal, and the inclined side under the 
horizontal side. Thus, DC A is the angle of depression 
from C to A. 

12. An oblique angle is one, the plane of whose sides is 
oblique to a horizontal plane. 

13. All lines, which can be the object of measurement, 
must belong to one of the classes above named, viz.: 

1st. Horizontal lines: 

2d. Yertical lines: 

3d. Oblique lines. 



5 





66 ELEMENTS OF SURVEYING. [BOOK li 

14. All tlie angles may also be divided into three 
classes, viz.: 

1st. Horizontal angles: 

2d. Vertical angles; which include angles of elevation 
and angles of depression: and 

3d. Oblique angles, or those included by oblique lines 


OF THE MEASUREMENT OF LINES AND ANGLES. 

15. It has been shown (Bk. I., Sec. III., Art. 1), that at 
least one side and two of the other parts of a plane triangle 
must be given or known, before the remaining parts can 
be found by calculation. 

"When, therefore, distances are to be found, by trigono¬ 
metrical calculations, two preliminary steps are necessary : 

1st. To measure certain lines on the ground: 

2d. To measure such angles as may be necessary to de¬ 
termine the required parts. 


MEASURES FOR DISTANCES. 

16. Any tape, rod, or chain, divided into equal parts, 
may be used as a measure; and one of these equal parts 
is called the unit of the measure. The unit of a measure 
may be a foot, a yard, a rod, or any other ascertained 
distance. 

The measure in general use, is a chain of four rods oi 
sixty-six feet in length; it is called Gunter’s chain, from 
the name of the inventor. This chain is composed of 100 
links. Every tenth link from either end, is marked by a 
small attached brass plate, which is notched, to designate 
its number from the end. The division of the chain into 
100 equal parts, is a very convenient one, since the divi¬ 
sions or links are decimals of the whole chain, and in the 
calculations may be treated as such. 


SEC I] MEASUREMENT OF DISTANCES. 


67 


TABLE. 

1 chain = 4 rods =66 feet = 2 inches = 100 links. 

Hence, 1 link is equal to 7.92 inches. 

80 chains = 320 rods = 1 mile. 

40 chains = \ mile. 

20 chains — \ mile. 

17. Besides the chain, there are needed for measuring, 
ten marking pins, which should be of iron, each about ten 
inches in length and an eighth of an inch in thickness. 
These pins should be strung upon an iron ring, and this 
ring should be attached to a belt, to be passed over the 
right shoulder, suspending the pins at the left side. Two 
staves are also required. Each of these should be about six 
feet in length, and have a spike in the lower end to aid in 
holding it firmly, and a horizontal strip of iron to pre- 
vent the chain from slipping off; these staves are to be 
passed through the rings at the ends of the chain. 

TO MEASURE A HORIZONTAL LINE. 

18. At the point where the measurement is to be be¬ 
gun, place, in a vertical position, a signal staff, having a 
small flag attached to its upper extremity; and place an¬ 
other at the point where the measurement is to be termi¬ 
nated. These two points are generally called stations. 

Having passed the staves through the rings of the 
chain, let the ten marking pins and one end of the chain 
be taken by the person who is to go forward, and who is 
called the leader, and let him plant the staff as nearly as 
possible in the direction of the stations. Then, taking tho 
staff in his right hand, let him stand off at arm’s length, 
so that the person at the other end of the chain can align 
it exactly with the stations: when the alignment is made, 
let the chain be stretched and a marking pin placed; then 
measure a second chain in the same manner, and so on, 
until all the marking pins shall have been placed. When 
the marking pins are exhausted, a note should be made, 
that ten chains have been measured; after which, the 
marking pins are to be returned to the leader, and the 


68 


ELEMENTS OF SURVEYING. [BOOK II 


measurement continued as before, until the whole distance 
is passed over. It will be found desirable to fasten pieces 
of red cloth to the heads of the marking pins, that they 
may be more readily found in thick grass, brushwood, &c. 

G reat care must be taken to keep the chain horizontal,» 
and if the slope of the ground be too great to admit of 
measuring a whole chain at a time, a part of a chain only 
should be measured: the sum of all the horizontal lines so 
measured, is evidently the horizontal distance between the 
stations. 

For example, in measuring 
the horizontal distance between 
A and C, we first place a staff 
at A and another at b , in the 
direction towards C. Then 
slide up the chain on the staff 
at A until it becomes horizon¬ 
tal, and note the distance ah. 

Then remove the staves and place them at b and d : make 
the chain horizontal, and note the distance cd. Measure 
in the same manner the line fC\ the sum of the horizontal 
lines ab, cd , fC, is equal to AB , the horizontal distance be¬ 
tween A and C. 

19. The length of the chain should be compared, from 
time to time, with a standard kept for the purpose. 

To facilitate this comparison, let two stakes be driven 
m the ground, distant from each other one chain, and let 
nails be driven in the heads of the stakes to mark the ex 
act length of the standard. 

Marks made upon the coping of a wall will answer the 
same purpose. If it is found that any line has been mea¬ 
sured with a chain, either too short or too long, the mea¬ 
sured distance may be corrected by the following pro¬ 
portion : 

As the length of the chain 
: the length of the standard 

: : the measured distance 

► 

: the true distance. 













SEC. I] 


OF THE THEODOLITE 


69 


For the correction of areas we have this proportion, 

As the square of the length of the chain 

: the square of the length of the standard, 

: : the area found 

: the area required. 


MEASUREMENT OF ANGLES. 

20. We come now to the measurement of angles, and 
for this purpose several instruments are used. The one, 
however, which affords the most accurate results, and which 
indeed can alone be relied on for nice or extensive opera¬ 
tions, is called a Theodolite. This instrument only will be 
described at present; others will be subsequently explained. 


OF THE THEODOLITE. 

PI. 1. The theodolite is an instrument used to measure 
horizontal and vertical angles. It is usually placed on a 
tripod ABC\ which enters by means of a screw the lower 
horizontal plate DE\ and becomes firmly attached to the 
body of the instrument. Through the horizontal plate DE\ 
four small hollow cylinders are inserted, which receive 
four screws with milled heads, that work against a second 
horizontal plate, EG. The upper side of the plate DE 
terminates in a curved surface, which encompasses a ball, 
that is nearly a semi-sphere, with the plane of its base 
horizontal. This ball, which is hollow, is firmly connected 
with the smaller base of a hollow conic frustum, that 
passes through the curved part of the plate DE, and 
screws firmly into the curved part of the second horizontal 
plate FG. 

A hollow conic spindle passes through the middle of 
the ball, and the hollow frustum with which it is connect¬ 
ed. To this spindle, a third horizontal and circular plate 
HI, called the limb of the instrument, is permanently attached. 
Within this Spindle, and concentric with it, there is a sec¬ 
ond spindle, called the inner, or solid spindle. To this 
latter, is united a thin circular plate, called the vernier plate, 


70 


ELEMENTS OF SURVEYING. [BOOK II 


which rests on the limb of the instrument, and supports 
the upper frame-work. The two spindles terminate at the 
base of the spherical ball, where a small screw enters the 
inner one, and presses a washer against the other, and the 
base ol the ball. On the upper surface of the plate FG, 
rests a clamp which goes round the outer spindle, and 
which, being compressed by the clamp-screw K, is made 
fast to it. This clamp is thus connected with the plate 
FG. A small cylinder a, is fastened to the plate FG : 
through this cylinder a thumb-screw L passes, and Avorks 
into a small cylinder b, connected with the clamp. The 
cylinders b and a, admit of a motion round their axes, to 
relieve the screw L of the pressure which, would otherwise 
be occasioned by working it. 

Directly above the clamp, is the lower telescope MN. 
This telescope is connected with a hollow cylinder, which 
is worked freely round the outer spindle, by the thumb¬ 
screw P having a pinion working into a concealed cog¬ 
wheel, that is permanently fastened to the limb of the in¬ 
strument. By means of a clamp-screw Q , the telescope is 
made fast to the limb, when it will have a common motion 
with the limb and outer spindle. 

The circular edge of the limb is chamfered, and is gen 
erally made of silver, and on this circle the graduation for 
horizontal angles is made. In the instrument described, 
the circle is cut into degrees and half degrees; the degrees 
are numbered from 0 to 360. 

On the circular edge of the vernier plate, is a small 
plate of silver, called a vernier; this plate is divided into 
30 equal parts, and numbered from the line marked 0 to 
the left. Two levels, at right angles to each other, are 
attached to the vernier plate by small adjusting screws; 
one of the levels is seen in the figure. 

$ 

The vernier plate turns freely around with the inner 
spindle. It is made fast to the limb of the instrument by 
the clamp-screw S', after which the smaller motions are 
made by the tangent-screw T There is a compass on the 
vernier plate, that is concentric with, it, the use of which 
will be explained under the head compass. 


SEC. I] 


OF THE THEODOLITE. 


71 


Tlie frame-work which supports the horizontal axis of 
the vertical semicircle UV and the npper telescope, with 
its attached level, rests on the vernier plate, to which it 
is made fast by three adjusting screwy placed at the angu¬ 
lar points of an equilateral triangle. The vertical semi¬ 
circle UV ) is called the vertical limb; its motions are gov¬ 
erned by the thumb-screw Z ' which has a pinion, that 
works with the teeth of the vertical limb. On the face 
of the vertical limb, opposite the thumb-screw Z, the limb 
is divided into degrees and half degrees: the degrees are 
numbered both ways from the line marked 0. There is a 
small plate resting against the graduated face of the verti¬ 
cal limb, called the vernier; it is divided into SO equal 
parts, and the middle line is designated by 0. 

On the other face of the vertical limb, are two ranges 
of divisions, commencing at the 0 point, and extending 
each way 45°. The one shows the vertical distance of 
any object to which the upper telescope is directed, above 
or below the place of the instrument, in 100th parts of the 
horizontal distance: the other, the difference between the 
hypothenusal and base lines: the liypothenuse being sup¬ 
posed to be divided into one hundred equal parts : there¬ 
fore, by mere inspection, we can ascertain the number of 
links, which must be subtracted from every chain of an 
oblique line, to reduce it to a true horizontal distance. 

The supports of the upper telescope are called the 
wyes, and designated Y’s. Two loops, turning on hinges, 
pass over the telescope, and are made fast by the pins c 
and d ; these loops confine the telescope in the Y’s. By 
withdrawing the pins, and turning the loops on their 
hinges, the telescope may be removed for the purpose of 
being reversed in position; and in both situations, the tele¬ 
scope can be revolved in the Y's about its axis. 

In the telescopes attached to the theodolite, are two 
principal lenses, one at each end. The one at the end 
where the eye is placed, is called the eye-glass, the other 
the object-glass 

In order that the axis of the telescope may be directed 
to an object with precision, two spider's lines, or small 


72 


ELEMENTS OF SURVEYING. [BOOK IL 


hairs, are fixed at right angles to each other, and placed 
within the barrel of the telescope, and at the focus of the 
eye-glass. The vertical hair is moved by two small hori¬ 
zontal screws, one of which, f is seen in the figure; and 
the horizontal hair, by two vertical screws, g and h. 

Before using the instrument it must be adjusted , that is, 
the parts must be brought to their proper relative positions: 
there are four principal adjustments. 

First adjustment. — To fix the intersection of the sjnder’s 
lines in die line of collimation or axis of the telescope. 

Having screwed the tripod to the instrument, extend 

the legs, and place them firmly. Then loosen the clamp- 

screw /S of the vernier plate, and direct the telescope to a 

small, well-defined, and distant object. By means of a 

small pin i, on the under side of the telescope, slide the 

eye-glass till the spider’s lines are seen distinctly; then with 

the thumb-screw X ’ which forces out and draws in, the 

\ ' # ' 
object-glass, adjust this glass to its proper focus, when the 

object, as well as the spider’s lines, will be distinctly seen: 

after which, by the tangent-screw T and the thumb-screw 

Z ) bring the intersection of the spider’s lines exactly upon 

a well-defined point of the object. 

Having done this, revolve the telescope in the Y's half 
round, when the attached level mn, will come to the upper 
side. See, in this position, if the horizontal hair appears 
above or below the point, and in either case, loosen one, 
and tighten the other, of the two screws that work the 
horizontal hair, till the horizontal hair has been carried 
over half the space between its last position and the ob¬ 
served point. Carry the telescope back to its place; di¬ 
rect again the intersection of the spider’s lines to the point, 
and repeat the operation till the horizontal hair neither 
ascends nor descends, while the telescope is revolved. A 
similar process will arrange the vertical hair, and the line 
of collimation is then adjusted. 

Second adjustment.— To make the axis of the attached 
level of the upper telescope , parallel to the line of collimation. 

Turn the vernier plate, till the telescope comes directly 


SEC. I] 


OF THE THEODOLITE 


73 


over two of the levelling screws, between the plates DE 
and FG. Turn these screws contrary ways, keeping them 
firm against the plate FG, till the bubble of the level mn , 
stands at the middle of the tube. Then, open the loops, 
and reverse the telescope. If the bubble still stands in the 
middle of the tube, the axis of the tube is horizontal; but 
if not, it is inclined, the bubble being at the elevated end. 
In that case, by means of the small vertical screws m and 
n, at the ends of the level, raise the depressed end, or de¬ 
press the elevated one, half the inclination; and then, with 
the levelling screws, bring the level into a horizontal posi¬ 
tion. Reverse the telescope in the Y’s, and make the 
same correction again; and so on, until the bubble stands 
in the middle of the tube, in both positions of the tele¬ 
scope : the axis of the level is then horizontal. Let the 
telescope be now revolved in the Y's. If the bubble con¬ 
tinue in the middle of the tube, the axis of the level is 
not only horizontal, but also parallel to the line of colli¬ 
mation. If, however, the bubble recede from its centre, 
the axis of the level is inclined to the line of collimation, 
and must be made parallel to it by means of two small 
antagonistic screws, (one of which is seen at p,) which work 
horizontally. By loosening one of them, and tightening 
the other, the level is soon brought parallel to the line of 
collimation, and then, if the telescope be revolved in the 
Y's, the bubble will continue in the middle of the tube. 

It is difficult to make the first part of this adjustment, 
while the axis of the level is considerably inclined to the 
line of collimation; for, if the level were truly horizontal 
in one position of the telescope, when the telescope is re¬ 
versed, the bubble would not stand in the middle of the 
tube, except in one position of the level. This suggests 
the necessity of making the first part of the adjustment 
with tolerable accuracy; then, having made the second 
with care, let the first be examined, and proceed thus till 
the adjustment is completed. 

Third adjustment. — To make the axes of the levels on 
the limb perpendicular to the axis of the instrument. 

This adjustment is effected, partly by the levelling 


74 


ELEMENTS OF SURVEYING [BOOK II 


screws, and partly by the tliumb-screw Z. Turn tlie ver¬ 
nier plate, until the upper telescope comes directly over 
two of the levelling screws, then turn them contrary ways, 
till the upper telescope is horizontal; after which, turn the 
vernier plate 180°, and if the bubble of the level remains 
in the middle of the tube, one line of the limb is horizon 
tal. But if the bubble recede from the centre of the level, 
raise the lower, or depress the upper end, one-lialf by the 
levelling screws, the other by the thumb-screw Z , till it is 
brought into a horizontal position. Turn the vernier plate 
again 180°, and if the level be not then horizontal, make 
it so, by dividing the error as before, and repeat the op¬ 
eration until the line of the limb is truly horizontal. 
Then turn the vernier plate 90°, and level as before. 
The limb ought now to be truly horizontal; but lest the 
first horizontal line may have been changed, in obtaining 
the second, it is well to bring the telescope and level two 
or three times over the levelling screws, until an entire 
revolution can be made without displacing the bubble from 
the middle of the tube. As this can only be the case 
when the level revolves around a vertical line, it follows 
that the limb will then be horizontal, and the axis of the 
instrument vertical. Then, by means of the small screws at 
the ends of the levels, bring the bubbles to the centres, and 
the axes of the levels will then be perpendicular to the axis 
of the instrument. 

Fourth adjustment.— To make the axis of the vertical 
lirnb perpendicular to the axis of the instrument. 

Bring the intersection of the spider's lines of the upper 
telescope upon a plumb line, or any well-defined vertical 
object, and move the telescope with the thumb-screw Z: 
if the intersection of the spider’s lines continue on the ver¬ 
tical line, the axis is horizontal. 

Or, the adjustment may be effected thus: Direct the 
intersection of the spider’s lines to a well-defined point 
that is considerably elevated : then turn the vertical limb, 
until the axis of the telescope rests on some other well-de¬ 
fined point, upon or near the ground: reverse the tele¬ 
scope, and turn the vernier plate 180°; now, if in elevating 
and depressing the telescope, the hue of collirnation passes 


SEC. 1.J 


75 


VERNIERS. 

through the two points before noted, the axis is horizontal. 
If it be found, by either of the above methods, that the 
axis is not horizontal, it must be made so by the screws 
which fasten the frame-work to the vernier plate. 

There are two important lines of the theodolite, the po¬ 
sitions of which are determined with great care by the 
maker, and fixed permanently. First, the axis of the in¬ 
strument is placed exactly at right angles with the limb 
and vernier plate; and unless it have this position, the 
vernier plate will not revolve at right angles to the axis, 
as explained in the third adjustment. Secondly, the line 
of collimation of the upper telescope is fixed at right angles 
to the horizontal axis of the vertical limb. We can as¬ 
certain whether these last lines are truly at right angles, 
by directing the intersection of the spider’s lines to a well- 
defined point; then removing the caps which confine the 
horizontal axis in its supports, and reversing the axis: if 
the intersection of the spider’s lines can be made to cover 
exactly the same point, without moving the vernier plate, 
the line of collimation is at right angles to the axis. 

If the theodolite be so constructed that either of the 
Y'a admits of being moved laterally, so as to vary the 
angle between the horizontal axis and the line of collima¬ 
tion, these lines may be adjusted at right angles to each 
other, if they have not been so placed by the maker. 

The lower telescope being used merely as a guard, re¬ 
quires no adjustment, although it is better to make the 
axis, about which its vertical motions are performed, hori¬ 
zontal, or perpendicular to the axis of the instrument; and 
this is easily effected by means of the two small screws 7c 
and Z, which work into the slide A\ that is connected with 
the horizontal axis. 

Having explained the methods of properly adjusting the 
theodolite, we will now explain the particular uses of its 
several parts, and the manner of measuring angles. 


VERNIERS. 

21. Before explaining the vernier, as applied to the the 
odolite, we shall discuss the general theory of verniers. 



70 


ELEMENTS OF SURVEYING. [BOOK IL 


A Yernier is a contrivance for measuring parts of the 
equal spaces marked off on a given scale or limb. 

It is a graduated scale, so arranged, as to cover an ex¬ 
act number of equal spaces on the primary scale or limb , 
to which it is applied. It is divided into a number of 
equal parts, greater by one than the number of equal spaces 
which it covers on the limb. 

The vernier may be applied to any scale of equal parts. 
The modes of its application are extremely various; the 
principle, however, is the same in all, and may be illus- 
trated by a simple diagram. 


8 & JO fj 12 13 1+ 15 16 17 18 19 














G 









1 

n 


0J234-56789 10 


Let AB be any limb or scale of equal parts, one of 
which let us suppose equal to b. Let CD be a vernier , 
equal in length to nine of these parts, and itself divided 
into ten equal spaces, each one of which is then equal to 
nine-tenths of b. The difference between a space on the 
limb and a space on the vernier, is therefore equal to one- 
tenth of b or b . This is the least space that can be meas¬ 
ured by means of the vernier, and is called the least count; 
hence, 

The least count of a vernier is equal to one of the equal 
divisions of the limb divided by the number of spaces on the 
vernier. 

22. The true reading of the instrument, for any position 
of the vernier, expresses the distance from the point where 
the graduation on the limb begins, marked 0, to the 0 
point of the vernier. In the diagram, that distance is ex¬ 
pressed by nine units of the scale, or 9. 

If, now, the vernier be moved till the division 1 coin 
cides with the division 10 of the limb, the 0 point will 
have advanced along the limb a distance equal to 
and the reading will become 9 4- fo^- If we again 
move the vernier till the division 2 coincides with the di¬ 
vision 11 of the scale, the 0 point will have advanced an 
additional distance, equal to and the reading becomes 


























SEC. I.J 


MEASUREMENT OF ANGLES 


77 


9 + Yob ; when 3 coincides with division 12, the reading 
will become 9 + j^b, and so on, till finally, when the point 

10 coincides with 19 of the scale, the distance 9 will have 
been increased by ^§5, and will become 10, as it should, 
since, in that case, the 0 point will have been moved a whole 
space, and will coincide with the division 10 of the limb. 
Hence, the following rule for reading an instrument which 
has a vernier. 

Read the limb in the direction of the graduation up to the 
division line next preceding the 0 point of the vernier; this 
is called the reading on the limb. Looh along the vernier till 
a dividing line is found to coincide with a line of the limb: 
multiply the number of this first line by the least count of the ver¬ 
nier: this is the reading on the vernier: the sum of these two 
readings is the reading of the instrument. 

23. In the theodolite described, the limb is divided into 
half degrees, and 30 spaces on the vernier cover 29 spaces 
on the limb. Hence, the least count of this instrument is 
5 ^ of a half degree or 1'. Fig. 2, Plate 1, exhibits the 
vernier of the horizontal limb, and Fig. 3 the vernier of 
the vertical limb. 


TO MEASURE A HORIZONTAL ANGLE WITH THE THEODOLITE. 

24. Place the axis of the instrument directly over the 
point at which the angle is to be measured. This is ef¬ 
fected by means of a plumb, suspended from the plate 
which forms the upper end of the tripod. 

Having made the limb truly level, place the 0 of the 
vernier at 0 or 360° of the limb, and fasten the clamp- 
screw S of the vernier plate. Then, facing in the direc¬ 
tion between the lines which subtend the angle to be mea¬ 
sured, turn the limb with the outer spindle, until the tele¬ 
scope points to the object on the left, very nearly. Clamp 
the limb with the clamp-screw If and by means of the 
tangent screws L and Z\ bring the intersection of the 
spider’s lines to coincide exactly with the object. 

Having loosened the clamp-screw Q of the lower tele¬ 
scope AIN. direct it with the thumb-screw P to the 


f 


78 ELEMENTS OF SURVEYING. [BOOK II 

same object at which the upper telescope is directed; then 
tighten the clamp-screw Q. This being done, loosen the 
clamp-screw S of the vernier plate, and direct the telescope 
to the other object: the arc passed over by the 0 point 
of the vernier, is the measure of the angle sought. 

The lower telescope having been made fast to the limb, 
will indicate any change of the position of the limb, should 
any have taken place; and, as the accuracy of the mea¬ 
surements depends on the fixedness of the limb, the lower 
telescope ought to be often examined, and if its position has 
been altered, the limb must be brought back to its place by 
the tangent-screw L. 

It is not necessary to place the 0 point of the vernier 
at the 0 point of the limb, previously to commencing the 
measurement of the angle, but convenient merely; for, 
whatever be the position of this point on the limb, it is 
evident that the arc which it passes over is the true mea¬ 
sure of the horizontal angle. If, therefore, its place be 
carefully noted for the first direction, and also for the sec¬ 
ond, the difference of these two readings will be . the true 
angle, unless the 0 point of the vernier shall have passed 
the 0 point of the limb, in which case the greater reading 
must be subtracted from 360°, and the remainder added to 
the less.' 


TO MEASURE A VERTICAL ANGLE. 

25. We shall first explain the method of determining 
the index error. Having levelled the horizontal limb, di¬ 
rect the telescope to some distinctly marked object as the 
top of a chimney, and read the instrument. Reverse the 
telescope in the Y’s, and turn the vernier plate 180°, and 
having directed the telescope to the same object, again 
read the instrument. If the two readings are the same, 
the limb is adjusted; that is, the 0 of the limb coincides 
with the 0 of its vernier, when the axis of the telescope 
is parallel to the horizontal limb. 

When the reading found with the eye end of the tele¬ 
scope nearest the vernier, is greater than that obtained in 
the reversed position, the true elevation of the object 


SEC. I] 


PRACTICAL PROBLEMS. 


79 


which is equal to a mean of the readings, may be obtained 
by subtracting half their difference from the first reading. 
If the first reading is less than the second, the half differ¬ 
ence must be added to the first. Hence, 

To find the index error , take the reading of the limb when 
the telescope is directed to a fixed object, first with the eye end 
of the telescope nearest the vernier , and then with the telescope 
and vernier plate both reversed. Take half the difference of 
these readings , and affect it with a minus sign if the first is 
greater, or a plus sign if the second is the greater; this is equal 
to the index error. 

Let the operation be repeated several times, using dif¬ 
ferent objects, and a mean of the errors will be more cor¬ 
rect than the result of a single observation. 

26. Having determined the index error, let the axis of 
the telescope be directed to any point either above or be¬ 
low the plane of the limb, and read the arc indicated by 
the 0 of the vernier. To the arc so read apply the proper 
correction, if any, and the result will be the true angle of 
elevation or depression. 

The angle of elevation may be more correctly found by 
taking the elevation of the object, and repeating the obser¬ 
vation with the telescope and vernier plate reversed, and 
then taking a mean of the readings for the angle required. 

MEASUREMENTS WITH THE TAPE OR CHAIN ONLY. 

27. It often happens that instruments for the measur 
ment of angles cannot be easily obtained; we must then 
rely entirely on the tape or chain. 

We now propose to explain the best methods of deter¬ 
mining distances, without the aid of instruments for the 
measurement of horizontal or vertical angles. 

I. To trace , on the ground , the direction of a right line ) that 

shall be perpendicular at a given point , to a given right 

line. 

FIRST METHOD. 

28. Let j BO be the given right line, and A the given 


80 


ELEMENTS OF SURVEYING. [BOOK IL 


point. Measure from A, on the 
line BC', two equal distances AB , 

AC, one on each side of the point 
A. Take a portion of the chain 
or tape, greater than AB, and 
place one extremity at B, and with the other trace the arc 
of a circle on the ground. Then remove the end which 
was at B, to C, and trace a second arc intersecting the 
former at D. The straight line drawn through D and A 
will be perpendicular to BC at A. 


D 

t 


Ji 


SECOND METHOD. 


29. Having made AB = AC, take D 

any portion of the tape or chain 
considerably greater than the dis¬ 
tance between B and C. Mark 
the middle point of it, and fasten 
its two extremities, the one at B 
and the other at C. Then, taking the chain by the middle 
point, stretch it tightly on either side of BC, and place a 
staff at D or E : DAE will be the perpendicular re¬ 
quired. 



THIRD METHOD. 

30. Let AB be the given line, 
and C the point at which the per¬ 
pendicular is to be drawn. From 
the point C measure a distance CA A 
equal to 8. With C as a centre, 
and a radius equal to 6, describe 
an arc on either side of AB : then, 
with i as a centre, and a radius equal to 10, describe a 
second arc intersecting at E, the one before described: 
then draw the line EC, and it will be perpendicular to 
AB at C 

s Bemark. Any three lines, having the ratio of 6 , 8, and 
10, form a right-angled triangle, of which the side corre¬ 
sponding to 10 is the liypothenuse. 


f 


c 











SEC. I.J 


SURVEYING CROSS. 


81 


FOURTH METHOD. 

31. Let AD be the given right 
line, and D the point at which 
the perpendicular is to be drawn. 

Take any distance on the tape 
or chain, and place one extrem- A 
ity at D , and fasten the other 
at some point, as E ) between 
the two lines which are to form the right angle. Place a 
staff at E. Then, having stationed a person at D , remove 
that extremity of the chain and carry it round until it 
ranges on the line DA at A. Place a staff at A : then 
remove the end of the chain at A, and carry it round 
until it falls on the line AE at F. Then place a staff at 
F ; ADF will be a right angle, being an angle in a 
semicircle. 

32. There is a very simple instrument, used exclusively 

in laying off right angles on the ground, which is called 
the ' 



SURVEYING CROSS. 

PI. 2, Fig. 1. This instrument consists of two bars, AB 
and CD, permanently fixed at right angles to each other, 
and firmly attached at E to a pointed staff, which serves 
as a support. Four sights are screwed firmly to the bars, 
by means of the screws a , b , c, and d. 

As the only use of this instrument is to lay off right 
angles, it is of the first importance that the lines of sight 
be truly at right angles. To ascertain if they are so, let 
the bar AB be turned until its sights mark some distinct 
object; then look through the other sights, and place a 
staff on the line which they indicate: let the cross be then 
turned until the sights of the bar AB come to the same 
line: if the other sights are directed to the first object, the 
lines of sight are exactly at right angles. 

The sights being at right angles, if one of them be 
turned in the direction of a given line, the other will mark 
the direction of a line perpendicular to it, at ! the point 
where the instrument is placed. 

6 





82 


ELEMENTS OP SURVEYING. [BOOK II 


IL From a given point without a straight line, to let fall a 

perpendicular on the line. 

33. Let C be the given point, and AB the given line. 
From C measure a line, as 
CA, to any point of the line AB. 

From A , measure on AB any 
distance as AF, and at F erect 
FE perpendicular to AB. 

Having stationed a person at A, measure along the per 
pendicular FE until the forward staff is aligned on the line 
AC: then measure the distance AE. How, by similar tri¬ 
angles, we have, 

AE : AF : : AC : AD, 

in which all the terms are known except AD, which may, 
therefore, be found. The distance AD being laid off from 
A , the point D, at which the perpendicular CD meets AB , 
becomes known. If we wish the length of the perpen¬ 
dicular, we use the proportion, 

AE : EF : : AC : CD, 

in which all the terms are known, excepting CD : there¬ 
fore, CD may be determined. 



III. To determine the horizontal distance from a given point to 

an inaccessible object. 


FIRST METHOD. 

34. Let A be an inaccessible object, and E the 
from which the distance is to be measured. 

At E lay off the right angle 
AED, and measure in the di¬ 
rection ED, any convenient dis¬ 
tance to D, and place a staff 
at D. Then measure from E, 
directly towards the object A, 
a distance EB of a convenient 8 . 
length, and at B lay off a line D F 
BC perpendicular to EA. Measure along the lin 


point 


* 

I 


A 


B 


E 


BC, 














BEG. I] 


PRACTICAL PROBLEMS. 


83 


until a person at D shall range the forward staff on the 
line DA. Now, DF is known, being equal to the differ* 
ence between the two measured lines DE and GB. Hence, 
by similar triangles, 

DF : FC :: DE : EA, 

in which proportion all the terms are known, except the 
fourth, which may, therefore, be found. 

SECOND M 

35. At the point E lay off 
EB perpendicular to the line 
EA, and measure along it any 
convenient distance, as EB. 

At B lay off the right an¬ 
gle EBD , and measure any dis¬ 
tance in the direction BD. Let 
a person at D align a staff on 
DA, while a second person at B aligns it on BE: the 
staff will thus be fixed at C. Then measure the dis¬ 
tance BC. 

The two triangles BCD and CAE being similar, wo 
have, 

BO : BD :: CE : EA, 

m which all the terms are known, except the fourth, which 
may, therefore, be found. 

THIRD METHOD. 

36. Let B be the given point, and A the inaccessible 
object; it is required to find BA. 

Measure any horizontal base 
line, as BC. Then, having 
placed staves at B and C, 
measure any convenient dis¬ 
tances BD and CE, such that 
the points D, B, and A, shall 
be in the same right line, as 
also, the points E, C, and A ; 
then measure the diagonal lines 
DC and EB. 



:thod. 

























84 


ELEMENTS OF SURVEYING. [BOOK II 


Now, in the triangle BEC\ 
the three sides are known, 
therefore, the angle ECB can 
be found. In the triangle CDB, 
the three sides are also known, 
therefore the angle CBD can be 
determined. These angles be¬ 
ing respectively subtracted from 
180°, the two angles ACB and 
A B C become known; and hence, 
in the triangle ABO,\ we have two 
side, to find the side BA. 



angles and the included 


IV To find the altitude of an object , when the distance to the 
vertical line passing through the top of it is known. 

87. Let CD be the altitude required, and A C the known 
distance. 

From A, measure on 
the line AC, any con¬ 
venient distance AB , and 
place a staff vertically 
at B. Then placing the 
eye at A ) sight to the 
object D, and let the 
point, at which the line AD cuts the staff BE, be marked. 
Measure the distance BE on the staff; then, 

AB : BE :: AO : CD , 

whence CD becomes known. 

If the line AC cannot be measured, on account of in¬ 
tervening objects, it may be determined by calculation, as 
in the last problem, and then, having found the horizontal 
distance, the vertical line is readily determined, as before. 


























BEC. IL] 


AREA OF LAND. 


85 


SECTION II. 

AREA OR CONTENTS OF GROUND.—LAYING OUT LAND. 

1. We come next to the determination of the area or 
superficial contents of ground. 

The surface of the ground being, in general, broken 
and uneven, it is impossible, without great trouble and ex¬ 
pense, to ascertain its exact area or contents. To avoid 
this inconvenience, it has been agreed to refer every sur¬ 
face to a horizontal plane: that is, to regard all its bound¬ 
ing lines as horizontal, and its area as measured by that 
portion of the horizontal plane which the boundary lines 
enclose. 

For example, if ABCD were a 
piece of ground having an uneven 
surface, we should refer the whole 
to a horizontal plane, and take 
for the measure of the area that 
part of the plane which is inclu¬ 
ded between the bounding hori¬ 
zontal lines AB , BC, CD, DA. 

In estimating land in this manner, the sum of the areas 
of all the parts into which a tract may be divided, is equal 
to the area, estimating it as an entire piece: but this would 
not be the case if the areas of the parts had reference to 
the actual surface, and the area of the whole were calcu 
lated from its bounding lines. 

2. The unit of measure of a quantity is a quantity ot 
the same kind regarded as a standard, and with which all 
quantities of that kind may be compared. For lines, the 
unit is a right line of a known length, as 1 foot, 1 link, 1 
chain, or any other fixed distance. 

It has been already observed (Bk. II., Sec. I., Art. 16), 
that Gunter’s chain of four rods or 66 feet in length, and 
which is divided into 100 links, is the chain in general 







88 


ELEMENTS OF SURVEYING. [BOOK II 


use among surveyors. In measuring land, the length of 
this chain is generally taken for the unit of linear measure, 


3. The unit of measure for surfaces is a square de¬ 
scribed on the unit of linear measure. 


1 foot. 


Thus, 1 square foot, 


1 square yard or 9 square feet, 


1 square chain, or 16 square rods. 


1 yard = 3 feet. 




When, therefore, the linear measures of ground are feet, 
yards, rods, or chains, the superficial measures are square 
feet, square yards, square rods, or square chains; and the 
numerical expression for the area is the number of times 
which the unit of superficial measure is contained in the 
land measured. 

4. An acre is a surface equivalent in extent to 10 square 
chains; that is, equivalent to a rectangle of which one side 
is ten chains, and the other side one chain. 

One quarter of an acre is called a rood. 

Since the chain is 4 rods in length, 1 square chain con¬ 
tains 16 square rods; and therefore, an acre, which is 10 
square chains, contains 160 square rods, and a rood con¬ 
tains 40 square rods. The square rods are called perches. 

5. Land is generally computed in acres, roods, and 
perches, which are respectively designated by the letters 
A. R. P. 
























S E C. I L] 


AREA OF LAND. 


87 


When the linear dimensions of a survey are chains or 
links, the area will be expressed in square chains or square 
links, and it is necessary to form a rule for reducing this 
area to acres, roods, and perches. For this purpose, let us> 
form the following 


TABLE. 


Miles. 

Acres. 

Roods. 

Sq. Chains. 

Perches. 

Sq. Links. 

1 

640 

1 

2560 

4 

1 

6400.0 
10.0 
* 2.5 

1.0 

102,400 

160 

40 

16 

1 

64,000,000 

100,000 

25,000 

10,000 

625 


1 square mile = 6400 square chains = 640 acres. 


Now, when the linear dimensions are links, the area 
will be expressed in square links, and may be reduced to 
acres by dividing by 100000, the number of square links 
in an acre: that is, by pointing off five decimal places 
from the right hand. 

If the decimal part be then multiplied by 4, and five 
places of decimals pointed off from the right hand, the 
figures to the left will express the roods. 

If the decimal part of this result be now multiplied by 
40, and five places for decimals pointed off, as before, the 
figures to the left will express the perches. 

If one of the dimensions be in links, and the other in 
chains, the chains may be reduced to links by annexing 
two ciphers : or, the multiplication may be made without 
annexing the ciphers, and the product reduced to acres and 
decimals of an acre, by pointing off three decimal places 
from the right hand. 

When both the dimensions are in chains, the product 
is reduced to acres by dividing by 10, or pointing off one 
decimal place. 

From which we conclude; that, 

1st. If links be multiplied by links , the product is reduced to 
acres by pointing of five decimal places from the right hard. 
















88 


ELEMENTS OF SURVEYING. [BOOK XL 


2d. If chains he multiplied hy links, the product is reduced 
to acres hy pointing off three decimal places from the right hand. 

3d. If chains he multiplied hy chains, the product is reduced 
to acres hy pointing off one decimal place from the right hand. 

6. Since there are 16.5 feet in a rod, a square rod is 
equal to . 16.5x 16.5 = 272.25 square feet. 

If the last number be multiplied by 160, we shall have, 

272.25 X 160 = 43560 = the square feet in an acre. 

Since there are 9 square feet in a square yard, if the 
last number be divided by 9, we obtain, 

4840 = the number of square yards in an acre. 


PROBLEM i. 

7. To find the area of a piece of ground in the form 
of a square, rectangle, or parallelogram. 

Multiply the hcise by the altitude , and the product will express 
the area (Geom., Bk. IV., Prop. IV. and V.) 

1. To find the area of the rectangular j) q 

field ABGD. ’ 

Measure the two sides AB , BG : let us 
suppose that we have found AB = 14 chains 
27 links, and BC= 9 chains 75 links. Then, A B 

AB= 1427 links, 

BG — 975 links, 

ABx BC= 1391325 square links, 

= 13.91325 acres. 

4 

3.65300 roods, 

40 

26.12000 perches. 

Ans. 13 A. 3 B. 26P. 

2. What is the area of a square field, of which the 
sides are each 33 ch. 8 1.? 




Ans. 109A IB. 29P. 







SEC. II.] 


AREA OF LAND. 


89 


8. What are the contents of a rectangular field, of which 
the longer side is 49 eh. 27 1., and the shorter 88 eh. 71.? 

Ans. 187A 2P. IIP. 


4. What are the contents of a field in the form of a 
parallelogram, of which the base is 85 ch. 65 1., and alti¬ 
tude 51 ch. 41.? 

Ans. 181A 3P. 33P. 


PROBLEM II. 

8. To find the contents of a piece of land in the form 
of a triangle. 


FIRST METHOD. 

Measure either side of the triangle 
as BC ) and from the opposite angle 
A let fall a perpendicular AD, and 
measure this perpendicular; then , mul¬ 
tiply the base and perpendicular to - 
gether, and divide the product by 2, 
the result will express the area of the triangle. Or , the area 

is equal to the base multiplied by half the perpendicular , or to 
the perpendicular multiplied by half the base (Geom., Bk. IV., 
Prop. VI.). 

1. What are the contents of a triangle whose base is 
25 ch. 1 1., and perpendicular 18 ch. 14 1. ? 

Ans. 22 A. 2 R. 29P. 

2. What are the contents of a triangle whose base is 
15.48 chains, and altitude 9.67 chains ? 

Ans. 7 A. IP. 38P. 


A 



SECOND METHOD. 

Measure two sides and their included angle. Then , add 
together the logarithms of the two sides and the logarithmic sine 
of their included angle; from this sum subtract the logarithm 
of the radius , which is 10, and the remainder will be the loga¬ 
rithmi of double the area of the triangle. Find , from the table. 




90 


ELEMENTS OF SURVEYING. [BOOK II 


the number answering to this logarithm, and divide it by 2 ; the 
quotient will be the required area (Geom. Mens., Art. 6). 

1. In a triangle ABC, suppose that we have found 
AB= 57.65 ch., A C— 125.81 eh., and the included angle 
CAB = 57° 25': required the area. 

Let the required area be designated b j then, 

" +log AB 57.65 . . . 1.760799 
+ log A C 125.81 . . 2.099715 
+ log sin A 57° 25' . 9.925626 

— log R .10 

= 6111.4 .... 3.786140. 

= 3055.7 square chains. 

Ans . 305A. 2 R. 11 P. 

Remark. In this example, the links are treated as de¬ 
cimal parts of the chain; the result, therefore, is in square 
chains and decimal parts of a square chain. 

2. What is the area of a triangle whose sides are 30 
and 40 chains, and their included angle 28° 57' ? 

Ans. 29 A. OR. 7 P. 


log 2 Q = 
2 Q 

And Q 


THIRD METHOD. 

Measure the three sides of the triangle. Then, add them 
together and take half their sum. From this half sum subtract 
each side separately. Then , multiply the half sum and the 
three remainders together , and extract the square root of the pro¬ 
duct: the result will be the area (Geom. Mens., Art. 7). 

Or, after having obtained the three remainders, add together 
the logarithm of the half sum and the logarithms of the re¬ 
spective remainders, and divide their sum by 2 .* the quotient 
will be the logarithm of the area. 

1. Find the area of a triangular piece of ground whose 
fiides are 20, 30, and 40 chains. 






SEC. II.] 


AREA OF LAND. 


91 


BY FIRST RULE. 

20 45 45 45 

30 -20 -30 -40 

40 25 1st rem. 15 2d rem. 5 3d rem. 

2)90 _ — — 

45 = half sum. Then, 

45 X ?,5 X 15 X 5 = 84375 : and -/8I375 = 290.4737 = tha 
area. 

Ans. 29 A. OR. 8P. 

2 What is the area of a triangle whose sides are 2569, 
4900, and 5035 links? 


BY SECOND RULE. 

2569 6252 6252 6252 

4900 -2569 - 4900 - 5035 

5035 3683 1st rem. 1352 2d rem. 1217 3d rem. 

2 )12504 ' ' 

6252 «= half sum. 


Then, 


log 6252 
log 3683 
log 1352 
log 1217 


Area in square h’nks, 6155225 


. 3.796019 
. 3.566202 
. 3.130977 
. 3.085291 
2)13.578489 
. 6.789244. 


.1 


Ans. 61 A. 2 R. 8P. 


PROBLEM III. 

9. To find the area of a piece of land in the form of 
a trapezoid. 

Measure the two parallel sides , and also the perpendicular 
distance between them. Add the two parallel sides together , 
and take half the sum ; then multiply the half sum by the 
perpendicular, and the product will be the area (Greom., Bk. 
17., Prop. VII.) 





















92 


ELEMENTS OF SURVEYING. [BOOK 11 


1. What is the area of a trapezoid, 
of which the parallel sides are 30 and 
49 chains, and the perpendicular distance 
between them 16 ch. 60 1., or 16.60 chains ? 

30 + 49 = 79; dividing by 2, gives . . 39.5 


multiply by . . •.16.60 

area in square chains. 655.700. 


Ans. 65+. 2P. IIP. 



2. Required the contents, when the parallel sides are 20 
and 32 ch., and the perpendicular distance between them 
26 ch. . ' PW 

Ans. 67A. 2P. 16P 


PROBLEM IV. 

10. To find the area of a piece of land in the form of 
a Quadrilateral. 

x 

Measure the four sides of the quadrilateral , and also one of 
the diagonals: the quadrilateral will thus he divided into two 
triangles, in both of which all the sides will he known. Then, 
find the areas of the triangles separately, and their sum will he 
the area of the quadrilateral. 

1. Suppose that we have measured 
the sides and diagonal AC,\ of the 
quadrilateral ABCD , and found 

AB = 40.05 ch. CD = 29.87 cli., 

BC = 26.27 ch. AD = 37.07 ch., 
and A C— 55 ch.: 

required the area of the quadrilateral. 

Ans. 101A IP. 15P. 

Remark. Instead of measuring the four sides of the 
quadrilateral, we may let fall the perpendiculars Bh , Dg, on 
the diagonal AC. The area of the triangle may then bo 
determined by measuring these perpendiculars and the di¬ 
agonal AC. The perpendiculars are Dg — 18.95 ck, and 
Bb = 17.92 ch. 


D 













• SEC. II] 


AREA OF LAND. 


93 


PROBLEM V. 

11. To find the contents of a field having any number 
of sides. 


Measure the sides of the field and also the diagonals: the 
three sides of each of the triangles into which the field will be 
thus divided will then be known , and the areas of the triangles 
may then be calculated by the preceding rules . Or, measure 
the diagonals , and from the angular points of the field draw 
perpendiculars to the diagonals and measure their lengths: the 
base and perpendicular of each of the triangles will then be 
known. 


1. Let it be required to determine the contents of the 
field ABODE\ having five sides. 



sured the diagonals and perpendicu¬ 
lars, and found, 

A 0= 36.21 ch., EO= 39.11 ch., 
Bb—4:.08 ch., Dd= 7.26 ch., 

.da = 4.19 ch.; required the area of the field. 



Area of triangle ABO— 73.8684 

square 

chains i 

area of 

“ CDE= 141.9693 

u 

u 

area of 

“ ACE= 81.7399 

<c 

u 

area of 

ABCDE= 297.5776 

u 

u 


Ans. 29 A. SB. IP. 


PROBLEM VI. 


12. To find the contents of a long and irregular figure, 
bounded on one side by a straight line. 

Suppose the ground, of which the contents are required, 
to be of the form ABEeda, bounded on one side by the 
right line AE\ and on the other by the curve edca. 


At A and A, the extremities of 
the right line AE, erect the two per¬ 
pendiculars Aa , Ee , and on each of 
them measure the breadth of the land. 
















94 


ELEMENTS OF SURVEYING. [BOOK IL 


Then divide the base into any convenient number of equal 
parts, and measure the breadth of the land at each point 
of division. 

Add together the intermediate breadths and half the sum of 
the two extreme ones: then multiply this sum by one of the 
equal parts of the base line, and the product will be the re¬ 
quired area very nearly (Mens. Art. 11). 

1. The breadths of an irregular figure, at five equidis¬ 
tant places, being 8.20 ch., 7.40 ch., 9.20 eh., 10.20 ch., and 
8.60 chains, and the whole length 40 chains, required the 
area. 

8.20 4)40 

8.60 10 one of the equal parts. 

2 )1(180 “ 

8.40 mean of the extremes, 85.20 sum, 

7.40 _10 

9.20 area 352.00 square ch. 

10.20 

85.20 sum. 

Ans. 3 5A. 82 P. 

2. The length of an irregular piece of land being 21 ch., 
and the breadths, at six equidistant points, being 4.35 ch., 
5.15 ch., 8.55 ch., 4.12 ch., 5.02 ch., and 6.10 chains: re¬ 
quired the area. 

Ans. 9 A. 2 R. 80 P. 

3. The length of an irregular piece of land is 80 ch., 
and the breadths at nine equidistant points are 5.75 ch., 
6.12 ch., 4.80 ch., 5.09 ch., 8.87 ch., 5.17 ch., 6.00 ch., 
3.94 ch., and 5.95 ch.: what is the area? 

Ans. 40 A. 8R. 14P. 

4. The length of an irregular field is 39 rods, and its 

breadths at five equidistant places are 4.8, 5.2, 4.1, 7.3, and 
7.2 rods: what is its area ? Ans. 220.35 sq. rods. 

Remark. If it is not convenient to erect the perpen¬ 
diculars at equal distances from each other, the areas of 
the trapezoids, into which the whole figure is divided, 
must be computed separately; their sum will be the re* 
quired area. 








SEO. II] 


AREA OF LAND. 


95 


PROBLEM VII. 

13. To find the area of a piece of ground in the forra 
of a circle. 


Measure the radius AC: then multiply 
the square of the radius by 3.1416 (Mens., 
Art. 15.). 



1. To find the area of a circular piece of land, of which 
the diameter is 25 ch. 


Ans. 49 A. OR. 14P. 


PROBLEM VIII. 

14. To find the contents of a piece of ground in the 
form of an ellipse. 


Measure the semi-axes AE\ CE. Then 
multiply them together , and their product 

by 3.1416. 

1. To find the area of an elliptical piece of ground, of 
which the transverse axis is 16.08 ch., and the conjugate 
axis 9.72 ch. 

Ans. 12 A. 1 R. 4P. 

Bemark I. The following is the manner of tracing an 
ellipse on the ground, when the two axes are known. 

From Cj one of the extremities of the conjugate axis 
as a centre, and AE half the transverse axis as a radius, 
describe the arc of a circle cutting AE in the two points 
F and G: these points are called the foci of the ellipse. 

Then, take a tape, the length of which is equal to AB t 
and fasten the two ends, one at the focus F, the other at 
the focus G. Place a pin against the tape and move it 
around, keeping the tape tightly stretched: the extremity 
of the pin will trace the curve of the ellipse. 

Bemark II. In determining the contents of ground, in 
tfco examples which have been given, the linear dimensions 
have been taken in chains and decimals of a chain. 



)B 








96 


ELEMENTS OF SURVEYING [BOOK H 


If the linear dimensions were taken in terms of any 
other unit, they may be readily reduced to chains. For, 
a chain is equal to 4 rods, equal to 22 yards, equal to 66 
feet. Hence, 

1st. Rods may be reduced to chains and the decimal of a 
chain , by dividing by 4. 

2d. Yards may be reduced to chains and the decimal of a 
chain , by dividing by 22. 

3d Feet may be reduced to chains and the decimal of a 
chain , by dividing by 66. 

Remark III. If it is thought best to calculate the area, 
without reducing the linear dimensions to chains, the re¬ 
sult can be reduced to acres: 

1st. By dividing it by 160 when it is in square rodi 
(Art. 5). 

2d. By dividing it by 4840 when it is in square yards 
(Art. 6). 

3d. By dividing it by 43560 when it is in square feet 
(Art. 6). 


OF LAYING OUT LAND. 

15. The surveyor is often required to lay off a given 
quantity of land, in such a way that its bounding lines 
shall form a particular figure, viz., a square, a rectangle, a 
triangle, &c. He is also often called upon to divide given 
pieces of land into parts containing given areas, or bearing 
certain relations to each other. 

The manner of making such divisions must always de¬ 
pend on a judicious application of the principles of geom¬ 
etry to the particular case. 

If, for example, it were required to lay out an acre ol 
ground in a square form, it would first be necessary to 
find, by calculation, the side of such a square, and then to 
trace, on the ground, a figure bounded by four equal lines 
at right angles to each other. 


SEC. II.] 


LAYING OUT LAND. 


97 


PROBLEM I. 

16. To lay out a giyen quantity of land in a square 
form. 

Reduce the given area to square chains , or square rods: 
then extract the square root , and the result will he the side of 
the required square. This square being described on the ground , 
will be the figure required. 

1. To trace a square which, shall contain 15A. OR. 12 P. 

First, 15 A = 60 R = 2400P 

Add, 12P ; hence, 

15A OR 12P=2412P; the square root 

of which is 49.11. 

Therefore, if a square be traced on the ground, of which 
the side is 49.11 rods, it will be the required figure. 

2. To trace a square which shall contain 176A. IP. 24P 

First, 176^4 = 1760 square chains, 

1 R= 2.5 “ 

hence, 24P= 1.5 “ “ 

17 6 A IP 24P=1764 square chains: the square 
root of which is 42. Hence, if a square be traced on the 
ground, of which the side is 42 ch., it will be the required 
figure. 

PROBLEM II. 

17. To lay out a given quantity of land in a rectangu¬ 
lar form, having one of the sides of the rectangle given. 

Divide the given area,, reduced to square chains or square 
reds , by the given side of the required rectangle , and the quotient 
will be the other side. Then , trace the rectangle on the ground. 

1. To lay off 240 acres in a rectangular form, one of 
the sides being given, and equal to 80 rods. 

First, 240A = 2400 square chains = 88400 square rods. 

Then, 80)38400(480 rods; which is the required side 
of the rectangle. 

18. A great number of similar problems might be pro¬ 
posed. The solution of them does not, however, properly 
belong to surveying. The laying out of the ground, and 

7 



98 


ELEMENTS OE SURVEYING. [BOOK II. 


the tracing of lines, after the figure and area have been 
determined, are the only parts which appertain to a prac¬ 
tical treatise. The manner of tracing lines having been ah 
ready explained, it seems unnecessary to add the numerous 
examples often given under this head of the subject. 


SECTION III. 

SURVEYING WITH THE COMPASS.—DIVIDING LAND. 

1. Before considering the principles involved in the 
method of surveying now to be explained, it will be ne¬ 
cessary to describe the instrument principally used in the 
field, and which is called 

THE CIRCUMFERENTER, OR SURVEYOR’S COMPASS. 

PL 2, Fig. 2. This instrument consists of a compass-box 
BCE\ a magnetic needle, a brass plate AB, from twelve to 
fourteen inches long, two plain sights, AF and BG, one 
of which is more fully shown in Fig. 3; and a stand, 
which is sometimes a tripod, and sometimes a single staff 
pointed with iron at the lower end, so that it may be 
placed firmly in the ground. 

The open sights, AF and BG , are placed at right an¬ 
gles to the plate AB, and fastened to it firmly by the 
screws a and b. In each sight there is a large and small 
aperture or slit; the larger aperture being above the smaller 
in one of the sights, and below it in the other. A hail 
or thread of silk is drawn vertically through the middle 
of the large aperture, as shown in Fig. 8. 

The compass-box DCF is circular, and generally about 
six inches in diameter. At the centre is a small pin, on 
which the magnetic needle is poised. This needle, if al¬ 
lowed to turn freely around the point of support, will settle 
to a state of rest: the direction which it then indicates, is 
that of the magnetic meridian. 



SEC. Ill] 


WITH THE COMPASS 


99 


In the interior of the compass-box, there is a graduated 
circle divided to degrees, and sometimes to half degrees: 
the degrees are numbered from the extremities of the di¬ 
ameter NS, both ways to 90°. 

The length of the magnetic needle is a little less than 
the diameter of the graduated circle, so that the needle can 
move freely around its centre, within the circle, and its 
positions be noted on the graduated arc. 

The compass-box is turned about its centre, without 
moving the plate AB, by means of the milled screw L : 
it is fastened to the plate AB , by the screw P. 

In using the compass, it is important to ascertain the 
exact angle which may be included between the magnetic 
meridian and the direction that may be given to the line 
drawn through the eye and the sights AF and BG. 

To effect this, a small arc HI is described on the bar 
AB , having its centre at the centre of the compass-box. 
This arc is divided to degrees, and sometimes to the parts 
of a degree. A vernier is also used, which is permanently 
attached to the compass-box. 

When the 0 point of this vernier coincides with the 0 
point of the graduated arc HI, the line of the compass-box 
marked NS, lies in the plane of the sights. 

Now, supposing the 0 of the vernier to coincide with 
the 0 of the arc HI, if the end of the needle does not 
stand at one of the lines of division of the graduated 
circle, let the whole degrees be read. Then, turn the 
compass-box by means of the screw L , until the needle 
points exactly to the line which marked the whole degrees: 
the space passed over by the 0 of the vernier, shows the 
parts of a degree that are to be added to give the true 
reading. 


SURVEYING WITH THE COMPASS. 

2. The line about which the earth revolves is called its 
axis; and the two points in which the axis meets the sui> 
face of the earth, are called the poles. 

3. A plane passed through the axis is called a meridian 


100 


ELEMENTS OF SURVEYING. [BOOK II 


plane, and its intersection with the surface is called a me¬ 
ridian line or a meridian. 

4. All the meridians converge towards the poles, but 
they vary so little from parallelism within the narrow limits 
of surveys made with the compass, that they may, without 
error, be regarded as parallel straight lines. 

5. If a magnetic needle be suspended freely and allowed 
to settle to a state of rest, a vertical plane passed through 
its axis is called the plane of the magnetic meridian ; and its 
intersection with the surface of the earth is called the mag¬ 
netic meridian, or sometimes a North and South line. A 
line perpendicular to a North and South line is called an 
East and West line. 

6. A line traced or measured on the ground, is called 
a course; and the angle which this line makes with the 
meridian passing through the 
point of beginning, is called 
the bearing. 

Thus, if we start from the 
point A , and measure in the 
direction Add. the line AB is 
the course, and the angle NAB 
is the bearing. 

"When the course, like AB, falls between the north and 
east points, the bearing is read, north 46° east, and is 
written N. 46° E. 

When the course, like AC, falls between the north and 
west points, the bearing is read, north 30° west, and is 
written N. 30° W. 

When the course, like AF, falls between the south and 
east points,' the bearing is read, south 70° east, and is writ¬ 
ten S. 70° E. 

When the course, like AD, falls between the south and 
west points, the bearing is read, south 70° west, and is 
written S. 70° W. 

A course which runs due north, or due south, is desig¬ 
nated by the letter N or S; and one which runs due east, 
or due west, by the letter E or W. 


N 






SEC. III.] 


101 


WITH THE COMPASS.. 


7. If, after having passed over a course, the hearing is 
taken to the back station, this bearing is called the back 
sight , or reverse bearing . 

>• 

8. The perpendicular distance between the east and west 

lines drawn through the extremities of a course, is called 
the northing or southing , according as the course is run to¬ 
wards the north or south. This distance is also called the 
difference of latitude , or simply the latitude, because it shows 
the distance which .one of the points is north ,or south of 
the other. .. .• 


IN" 

' • n / 

'T7& 

i * • » 

-vT I 
/ • 

/ 


C 

G 


Thus, in running the course from A 
to B , AG is the difference of latitude, 
north. 

9. The perpendicular distance bd- YV^- fff- -dE 

tween the meridians passing through the 
extremities of a course, is called the de¬ 
parture of that course, and is east or g 

west, according as the course lies on 
the east or west side of the meridian passing through the 
point of beginning. 


Thus, in running the course AB ) CB is the 1 departure, 
east. 


10. It will be found convenient, in explaining the rules 
for surveying with the compass, to attribute to the lati¬ 
tudes and departures the algebraic signs, + and —. 

We shall, therefore, consider every northing as affected 
with the sign +, and every southing as affected with the 
sign —. We shall also consider every easting as affected 
with the sign +, and every westing as affected with the 
sign —. 

11. The meridian distance of a point is its perpendicular 
distance from an assumed meridian. Thus, if the distance 
be estimated from the meridian NS, BC will be the meri¬ 
dian distance of the point B. 

12. The meridian distance of a line is the meridian dis¬ 
tance of its middle point, and is east or west, according as 
this point lies on the east or west side of the assumed me- 





102 


ELEMENTS OF SURVEYING. [BOOK Ii 


ridian. Thus, FG drawn through the middle point of AB, 
is the meridian distance of the line AB. 

The sign + will always be given to the meridian dis¬ 
tance of a point or line, when it lies on the east of the as¬ 
sumed meridian, and the sign —, when it lies on the west. 

13. When a piece of ground is to be surveyed, we be¬ 
gin at some prominent corner of the field, and go entirely 
around the land, measuring the lengths of the bounding 
lines with the chain, and taking their bearings with the 
compass. It is not material whether the ground be kept 
on the right hand or on the left, and all the rules deduced 
for one of the cases, are equally applicable to the other. 
To preserve uniformity, however, in the language of the 
rules, we shall suppose the land to be always kept on the 
right hand of the surveyor. 


FIELD OPERATIONS. 


14. Let A BCD be a piece of 
ground to be surveyed, A the point 
where the work is to be begun, 
and NS a meridian. 

On a sheet of paper, rule three 
columns, as follows, and head them 
stations, bearings, distances. 


Stations. 

Bearings. 

Distances. 

1 

N 31}° W 

10. 

2 

N 62J° E 

9.25 

3 

S 36° E 

7.60 

4 

S 45|° W 

10.40 


Place the compass at A t and take the bearing to B 
which is PAB: suppose this angle has been found to be 
S1 2 ° The bearing from A to B is then N. 31£° W. En* 


N 



A 

S 






















S EC. Ill] 


WITH THE COMPASS. 


103 


tor this bearing in the field notes opposite station 1. 
Then measure the distance from A to B, which we will 
suppose to be 10 ch., and insert that distance opposite sta¬ 
tion 1, in the column of distances. 

We next take the bearing from B to 0, N. 62J E., and 
then measure the distance BC—§ ch. 25 1., both of which 
we insert in the notes opposite station 2. 

At station C we take the bearing to D, S. 36° E., and 
then measure the distance CD — 7 ch. 60 L, and place them 
in the notes opposite station 8. 

At D we take the bearing to A, S. 45W., and mea¬ 
sure the distance DA = 10 ch. 40 1. We shall then have 
made all the measurements on the field which are neces¬ 
sary to determine the contents of the ground. 

15. Remark I. The reverse bearing or back sight, from 
B to A, is the angle ABU’, and since the meridians NS 
and HGr are parallel, this angle is equal to the bearing 
NAB. The reverse bearing is, therefore, S. 81J° E. 

The reverse bearing from G J is S. 62 W .; that is, it 
is the angle ICB = GBC. 

And generally, a reverse bearing, or back sight, is always 
equal to the forward bearing, and differs from it in both of the 
letters by which it is designated . 

16. Remark II. In taking the bearings with the com¬ 
pass, there are two sources of error. 1st. The inaccuracy 
of the observations: 2d. Local attractions, or the derange¬ 
ment which the needle experiences when brought into the 
vicinity of iron-ore beds, or any ferruginous substances. 

To guard against these sources of error, the reverse 
bearing should be taken at every station: if this and the 
forward bearing are of the same value, the work is proba¬ 
bly right; but if they differ considerably, they * should both 
be taken again. 

17. Remark III. If the forward and back sights at the 
end of any course of the survey agree, it may be safely 
assumed, that no local attraction disturbs the needle at 
these points; and hence, that the next foresight is also free 
from such disturbing causes. The e”ror, therefore, from 


104 


ELEMENTS OF SERVE TING. [BOOK IL 


local attraction, when it arises, will first show itself in the 
difference between a true foresight and an erroneous back 

o / 

sight. 

When this difference appears, subtract the back sight 
from the foresight, and call the difference the correction foi 
the next foresight. The correction will be positive when 
the foresight is the larger, and negative when it is less. 

Add this correction, with its proper sign, to the fore¬ 
sight of the next course, when the meridional and longitu¬ 
dinal letters of that course are both the same, or both dif¬ 
ferent from the foresight of the previous course, and sub¬ 
tract it when one of the letters is the same and the other 
different: the result will be the true bearing. The true 
bearing of any other course may be found by the same 
process. 


EXAMPLE. 


True Foresights. 

Back Sights. 

Foresights of next 
Course. 

Foresights 

Corrected. 

1. S 85° 10' W 

2. N 16° 20' E 

3. N 17° 25' TV 

4. S. 47° 18' E 

N 85° 05' E 
S 18° 20' W 
S 16° 10' E 
N 48° 10'W 

S 10° 15' W 
E 15° 25' TV 
E 28° 10' E 
S 49° 15' TV 

S 10° 20' IV 
E17° 25'TV 
N 27° 01' E 
N 50° 07' TV 


Note. —If there be no course in the survey in which 
the foreward and back sights agree, take the one in which 
they agree the nearest, and add half the difference of the 
bearings to the least, and treat the result as the true bearing 


18. Remark IV. In passing- 
over the course AB, the north¬ 
ing is found to be HB , and the 
departure, which is west, is repre¬ 
sented by AH. Of the course BC, 
the northing is expressed by BG , 
and the departure, which is east, 
by GC. Of the course CD, the 
southing is expressed by Cl, and 
the departure, which is east, by 
CF. Of the course DA, the south- 


N 
























SEC. Ill] 


TRAVERSE TABLE 


105 


ing is expressed by KA, and the departure, which, is west, 
by DK. It is seen from the figure, that the sum of 
the northings is equal to HB + BG = IIG; and that the 
sum of the southings is equal to CI+ KA=PA — HG : 
hence, the sum of the northings is equal to the sum of the 
muthings. 

If we consider the departures, it is apparent that the 
sum of the eastings is equal to GC+ CF = GF ; and that 
the sum of the westings is equal to AII-\- DK— GF ; hence 
also, the sum of the eastings is equal to the sum of the westings. 
We therefore conclude, that when any survey is correctly 
made, the sum of the northings will he equal to the sum of the 
southings , and the sum of the eastings to the sum of the 
westings. 

It would indeed appear plain, even without a rigorous 
demonstration, that after having gone entirely round a 
piece of land, the distance passed over in the direction due 
north, must be equal to that passed over in the direction 
due south; and the distance passed over in the direction 
due east, equal to that passed over in the direction due 
west. 

Having now explained the necessary operations on the 
field, we shall proceed to show the manner of computing 
the contents of the ground. We shall first explain, 



THE TRAVERSE TABLE AND ITS USES. 


19. This table shows the latitude and departure corres¬ 
ponding to bearings that are expressed in degrees and 
quarters of a degree from 0 to 90°, and for every course 
from 1 to 100, computed to two places of decimals. 

The following is the method of deducing the formulas 
for computing a traverse table; by means of these for¬ 
mulas and a table of natural sines, the latitude and depar¬ 
ture of a course may be computed to any desirable degree 
of accuracy. 


106 


ELEMENTS OF SURVEYING. [BOOK II 


Let AD represent any course, and 
NAD — ACB, expressed in degrees and 
minutes, be its bearing. Let AG be tbe 
unit of measure of the course, and also 
the radius of the table of natural sines 
(Bk I., Sec. III., Art. 14). Draw DE and 
CB parallel to ISIS, and AE perpen¬ 
dicular to A A. Then will DE be the 
latitude , and AE the departure of the course, and CB the co¬ 
sine ^ and AB the sine of the bearing. 

From similar triangles we have these proportions, 

AC : CB :: AD : DE, or 

1 : cos of the bearing : : course : latitude, 

AC : AB : : AD : AE, or 

1 : sin of the bearing : : course : departure. 

Whence, lat. = course X cos of the bearing, 
dep. = course X sin of the bearing. 

We have then the following practical rule for compu¬ 
ting the latitude and departure of any course. 

Look in a table of natural sines for the cosine and sine of 
the bearing. Multiply each by the length of the course, and the 
first product will be the latitude, and the second will be the 
departure of the given course. 



EXAMPLES. 

1. The bearing is 65° 39', the course 69.41 chains : what 


i3 the latitude, and what the departure? 

Natural cosine of 65° 39'.41231 

Length of the course.69.41 

Product, which is the Dif. of Latitude, 28.6184371. 

Natural sine of 65° 39'.91104 

Length of the course.69.41 

Product, which is the Departure . . 63.2352864. 













BEC. Ill] 


TRAVERSE TABLE. 


107 


2. The bearing is 75° 47', the course 89.75 chains: what 


is ihe latitude, and what the departure ? 

Natural cosine of 75° 47'.24559 

Length of course. . 89.75 

Product, which is the Dif. of Latitude, 22.0417025, 

Natural sine of 75° 47'.96937 

Length of course.89.75 

Product, which is the Departure . . 87.0009575. 


w 


c 

H , 

i~7U 

a 

—y'F | 

r 

/ h 

A 

J 


/ 


E 


20. In this manner the traverse table given at the end 
of the book has been computed. When the bearing is 
given in degrees and quarters of a degree, and the differ¬ 
ence of latitude and departure are required to only two 
places of decimals, they may be taken directly from the 
traverse table. 

If the bearing is less than 45°, the angle will be found 
at the top of the page; if greater, at the bottom. Then, 
if the distance is less than 50, it will be found in the col¬ 
umn “distance,” on the left hand page; if greater than 50, 
in the corresponding column of the right hand page. 

The latitudes or departures of courses 
of different lengths, but which have the 
same bearing, are proportional to the 
lengths of the courses. Thus, in the 
figure, the latitudes AG, AG , or the de¬ 
partures GF\ CB , are to each other as 
the courses AF\ AB. 

Therefore, when the distance is greater than 100, if 
may be divided by any number which will give an exact 
quotient, less than 100 : then the latitude and departure of 
the quotient being found and multiplied by the divisor, the 
products will be the latitude and departure of the v r hole 
course. It is also plain, that the latitude or departure of two 
or more courses, having the same bearing, is equal to the 
gum of the latitudes or departures of the courses taken sepa¬ 
rately. 

Hence, if we have any number greater than 100, as 
614, we have only to recollect that, 610 + 4 = 614; and 
also, that the latitude and departure of 610, are ten times 


s 















108 


ELEMENTS OF SURVEYING. [BOOK IL 


as great, respectively, as the latitude and departure of 
61: that is, equal to the latitude and departure of 61 mul¬ 
tiplied by 10, or with the decimal point removed one place 
to the right. 


EXAMPLES. 


1. To find the latitude and departure for the bearing 
294°, and the course 614. 


Latitude for 610 . 
Latitude for 4 . 

Latitude for 614 . 


. 530.90 
3.48 

. 534.38 


Departure for 610 . 
Departure for 4 . 

Departure for 614 . 


300.40 

1.97 

302.37 


In this example, the latitude and departure answering 
to the bearing 29and to the distance 61, are first taken 
from the table, and the decimal point removed one place 
to the right: this gives the latitude and departure for the 
distance 610; the latitude and departure answering to the 
same bearing and the distance 4, are then taken from the 
table and added. 


2. To find the latitude and departure for the bearing 
624°, and the course 7855 chains. 


Latitude for 7800 . 3602.00 Departure for 7800 . 6919.00 
Latitude for 55 . 25.40 Departure for 55 . 48.79 


Latitude for 7855 


. 3627.40 


Departure for 7855 . 6967.79 


Remark. When the distances are expressed in Avhole 
numbers and decimals, the manner of finding the latitudes 
and departures is still the same, except in pointing off the 
places for decimals: but this is not difficult, when it is re¬ 
membered that the column of distances in the table, may 
be regarded as decimals, by removing the decimal point to 
the left in the other columns. 


3. To find the latitude and departure for the bearing 
47|°, and the course 37.57. 


Latitude for 37.00 
Latitude for .57 

Latitude for 37.57 


• \ 


24.88 

.38 


Departure for 37.00 
Departure for .57 


25.26 


Departure for 37.57 


27.39 

.42 

27.81 























SEC, HI.] 


OF BALANCING. 


109 


OF BALANCING THE WORK. 

21. The use of the traverse table being explained, we 
can proceed to compute the area of the ground. 

The field notes having been completed, rule a new table, 
a= below, with four additional columns, two for latitude, 
and two for departure. 

Then find, from the traverse table, the latitude and de¬ 
parture of each course, and enter them in the proper col¬ 
umns opposite the station. 

Then add up the column of northings, and also the col¬ 
umn of southings: the two sums should be equal to each 
other. If they are not, subtract the less from the greater; 
the remainder is called the error in latitude. This error 
takes the name of that column which is the less. For 
example, if the sum of the northings is less than the sum 
of the southings, the error is called, error in northing: but 
if the sum of the southings is less than the sum of the 
northings, the error is called, error in southing. We find 
the error for each particular course by the following pro¬ 
portion. 

As the sum of the courses 
Is to the error of latitude, 

So is each particular course 
To its correction. 

The error thus found may be entered in a separate col¬ 
umn ; after which add it to the latitude of the course when 
the error and latitude are of the same name , but subtract 
it when they are of different names. This will make the 
sum of the northings equal to the sum of the southings, 
and is called balancing the work. The northings and south 
ings thus corrected are entered in columns on the right, 
under the head balanced. 

The eastings and westings are balanced in the same 
manner; the difference between their sums being called 
erroi in departure. 

For an example, we will resume the one already con¬ 
sidered. 


110 


ELEMENTS OF SURVEYING. [BOOK II 


Error in Northing 


0.68 





LATITUDE. 

DEPARTURE. 



BALANCED 

Sta. 

Bearings. 

Distan¬ 

ces.. 

N. 

+ 

S. 

E. 

+ 

W. 

Cor. 

Lat. 

Cor. 

Dep. 

N. 

+ 

S. 

E. 

+ 

W. 

1 

N 31 p W 

10. 

8.53 



5.22 

+ o id 

+ 0.02 

8.71 



5.24 

2 

N 62JO E 

9.25 

4.23 


8.22 


+ 0.17 

— 0.01 

4.40 


8.21 


3 

S 36° E 

7.60 


G.15 

4.47 


— 0.14 

— 0.01 


601 

4.46 


4 

S 45P w 

10.40 


7.29 


7.41 

—0.19 

+ 0.02 


7.10 


7.43 

Sum of courses, 37.25 

12.76 

1344 

12.76 

12.69 

12.63 

12.63 

13.11 

13.11 

12.67 

12.67 


0.06 Error in Westing. 


As 37.25 : 0.68 :: 10 : 0.18 error in lat. of 1st course 

As 37.25 : 0.68 :: 9.25 : 0.17 error in lat. of 2d course. 

As 37.25 : 0.68 :: 7.60 : 0.14* error in lat. of 3d course. 

As 37.25 : 0.68 :: 10.40 : 0.19 error in lat. of 4th course. 

As 37.25 : 0.06 : : 10 : 0.02* error in dep. of 1st course. 

As 37.25 : 0.06 :: 9.25 : 0.01 error in dep. of 2d course. 

As 37.25 : 0.06 :: 7.60 : 0.01 error in dep. of 3d course. 

As 37.25 : 0.06 :: 10.40 : 0.02 error in dep. of 4tli course. 

22. Remark I. In finding the error in latitude or de¬ 
parture, for a particular course, the last figure is sometimes 
doubtful: in which case it is best to mark it, as in the 
third proportion for error in latitude, and the first for er¬ 
ror in departure; and then, if the figures taken do not 
balance the work, let each be increased or diminished by 1. 

23. Remark II. It has already been observed (Art. 18), 
that if the measurements on the field be correctly made, 
the sums of the northings and southings will be eoual to 
each other, as also those of the eastings and westings. It 
is the opinion of some surveyors, that when the error in 
latitude or departure exceeds one link for every five chains 
of the courses, the field notes ought not to be relied on, 
This, perhaps, is a higher degree of accuracy than can be 
attained. The error, however, should always be made 
considerably less than one link to a chain. 

24. The following is an example in which the latitude 
and departure of each course have been computed from 
the table &f natural sines. 






















































BEC III] 


ur BALANCING 


111 


St*. 

Bearings. 

Dist. 

Dif. of Latitude. 

Departs e. 

Balanced. 

N. 

S. 

E. 

W. 

X. 

S. 

E. 

W. 

1 

O 1 

N 45 55 W 

63 ch. 

36.87210 



38.07149 

36.65908 



18.07149 

2 

N 4 50 2 

74.40 

74.13513 


6.26894 


73.72813 


6.26894 


3 

H 89 05 E 

125.50 

2.00800 


125.48368 


1.96126 


125.49228 


4 

S 1 60 W 

71.80 


71.76338 


2.29688 


72.17110 


2.29G88 

i 

S 7 40 E 

31.20 


30.92107 

4.16239 



31.12133 

4.16239 


< 

N 89 25 W 

35.50 

0.36139 



35.49822 

0.36139 



35.49822 

7 

S 84 35 W 

40. 


3.77600 


39.82120 


3.80352 


39.81260 

8 

S 74 35 W 

21. 


5.58264 


20.24442 


5.61385 


20.24442 


113.37662 112.04309 
112.04309' 

135.91501 

135.93221 

135.91501 

112.70986 

112.70985 

135.92361 

135.92361 


Error in Southing 1.33353 0.01720 Error in Easting. 

Half Error 0.66676 0.00860 Hall'Error. 


Instead of balancing by the method just explained, we 
divide each error by two. Now if we subtract half the 
error in southing from the column of northings, and at the 
same time add it to the column of southings, these two 
columns will exactly balance. In like manner, if we sub¬ 
tract half the error in easting from the column of westings, 
and at the same time add it to the column of eastings, 
these columns will also balance. 

The errors should be distributed in proportion to the 
lengths of the courses, but this may be done with sufficient 
accuracy without making the proportions. If any of the 
courses have been run over rough ground, the probability 
is that the errors belong to these courses, and they should 
be distributed among them. 

In this example we separate the half error in southing 
into the three parts .40700, .21302, and .04674, and subtract 
them respectively from the northings of courses 2, 1, and 
3, and then place the northings in the balanced columns. 
For the southings we separate the half error into the four 
parts .40772, .20031, .03121, and .02752, and add them respec¬ 
tively to the southings of the courses 4, 5, 8, and 7. We 
then enter the southings in the balanced columns. As the 
error in 'easting is so small, we add half of it to the east¬ 
ing of course 3, and subtract half from the westing of 
course 7. 



\ 







































112 


ELEMENTS OF SURVEYING. [BOOK II 


OF THE DOUBLE MERIDIAN DISTANCES OF THE COURSES. 


25. After tlie work lias been balanced, the next thing 
to be done is to calculate the double meridian distance of 
each course. 

For this purpose, a meridian line is assumed, lying 
either wholly without the land, or passing through any 
point within it. It is, however, most convenient to take 
that meridian which passes through the most easterly or 
westerly station of the survey; and these two stations are 
readily determined by inspecting the field notes. 

Having chosen the meridian, let the station through 
which it passes, be called the principal station , and the 
course which begins at this point, the first course. Care, 
however , must be taken, not to confound this with the cow'se 
which begins at station 1, and which is the first course that is 
entered in the field notes. 

It has already been remarked (Art. 10), that all de¬ 
partures in the direction east, are considered as plus , and 
all departures in the direction west as minus. 


N 


26. To deduce a rule for finding the double meridian 
distances of the courses. Let BC 
represent any course, and AB the 
preceding course; also, let B and 
E be their middle points. Draw 
Ell , CM, and DC, perpendicular to 
the assumed meridian NS. Draw 
also A I, EK ’ and BL, parallel to 
. NS. Then 2 DG is the double me¬ 
ridian distance of the course BC J 
and 2EII- 2 KG, is the double me¬ 
ridian distance of the course AB. 

How, 2BG—2GK + 2KL + 2LD ; but 2 KL = IL is the 
departure of the course AB, and 2LJD—MC is the depar¬ 
ture of the course BC : 



consequently, 2 GD = 2 GK + IL + MC\ 

hence, the double meridian distance of a course, is equal 
to the double meridian distance of the preceding course 








SEC. Ill] DOUBLE MERIDIAN DISTANCES 


113 


plus the departure of that course plus the departure of the 
course itself; if there is no preceding course, the first 
two terms become zero. We therefore have the following 

RULE. 

L The double meridian distance of the first course is equal 
to its departure. 

II. The double meridian distance of the second course is 
equal to the double meridian distance of the first course , plus 
its departure , plus the departure of the second course. 

III. The double meridian distance of any course is equal 
to the double meridian distance of the preceding course ) plus 
its departure , plus the departure of the course itself 

27. Remark. It should be recollected that plus is here 
used in its algebraic sense, and that when the double me¬ 
ridian distance of a course and the departure which is to 
be added to it, are of different names, that is, one east and 
the other west, they will have contrary algebraic signs; 
hence, their algebraic sum will be expressed by their dif¬ 
ference, with the sign of the greater prefixed to it. 

If the assumed meridian cuts the enclosure, the double 
meridian distances, estimated to the left, must be taken 
with the minus sign. 

The double meridian distance of the last course should 
be equal to the departure of that course. A verification 
of the work is, therefore, obtained by comparing this double 
meridian distance with the departure of the course. 

28. To apply the above rule to the particular example 
already considered (Art. 21), rule a new table as below, in 
which are entered the balanced northings and southings, and 
the balanced eastings and westings. 

In this table there is but a single column for the dif¬ 
ferences of latitude, and a single column for the departures. 
The 4- sign shows when the difference of latitude is north, 
and the — sign when it is south. The + sign also shows 
when the departure is east, and the — sign when it is west. 

8 


114 


ELEMENTS OF SURVEYING [BOOK II 


Sta. 

Bearings. 

Distances. 

Dif. Lat. 

Dep. 

D. M. D. 

1 

N 31*° W 

10. 

+ 8.71 

-5.24 

+ 17.91 

— 7.43 

— 5.24 






+ 5.24 

2* 

1ST 62f° E 

9.25 

+ 4.40 

+ 8.21 

8.21 

3 

S 86° E 

7.60 

-6.01 

+ 4.46 

+ 8.21 
+ 8.21 
+ 4.46 

4 

S 45W 

10.40 

-7.10 

-7.43 

+ 20.88 

+ 20.88 
+ 4.46 
— 7.43 






+ 17.91 


We see, from inspecting the notes, that 2 is the most 
westerly, and 4 the most easterly station. Either of them 
may, therefore, be taken for the principal station. Let us 
assume 2 for the principal station, and distinguish it by a 
star, thus *. 

Having done so, we enter the departure 8.21 in the 
column of double meridian distances, which gives the 
double meridian distance of the first course. The double 
meridian distances of the other courses are calculated ac¬ 
cording to the rule; and as the last, opposite to station 1, 
is equal to the departure of the course, the work is known 
to be right. 

29. Having shown the manner of computing the double 
meridian distance of each course, we shall now deduce a 
rule for finding the 

AKEA. 

Let us still consider the same 
example. We will first write the 
differences of latitude and the 
double meridian distances of the 
courses, in the following table 


N 

































THE AREA 


115 


SEC. Ill] 


r—~ 

Stations. 

Dif. of Latitude. 

D. M. D. 

Area. 

+ 

Area. 

1 

+ cB 

-f 2 ba 

2 cAB 


2* 

+ Bs 

+ 2 qp 

2 BsC 


3 

-yD 

4- 2?z/i 


2ms CD 

4 

-Df 

•4“ 2 ed 


2 cmDA 


It is evident, that cB multiplied by 2ba = cA, will give 
double the area of the triangle cAB. But cB and ba are 
both plus; hence, the product will be plus, and must be 
put in the column of plus areas. Double the area of 
the triangle BsC, is equal to Bs multiplied by 2qp, which 
product is also plus. 

The area of the trapezoid ms CD is equal to yD = ms 
multiplied by nh (Geom., Bk. IV., Prop. VII., S.); hence, 
double the area is equal to yD into 2nh. But since yD is 
minus, and 2 nh plus, it follows that the product will be 
negative; hence, it must be placed in the column of nega¬ 
tive areas. 

Double the area of the trapezoid cADm , is equal to 
w= me multiplied by 2 de : but, since Df is negative and 
2 de positive, the product will be negative. 

It is now evident that the difference between the two 
columns is equal to twice the contents of the figure ABCD : 
and since the same may be shown for any other figure, we 
may write, for finding the areas, the following general 

RULE. 

I. Multiply the double meridian distance of each course by 
its northing or southing, observing that like signs in the multi- 
plicand and multiplier give plus in the product, and that un¬ 
like signs give minus in the product. 

II. Place all the products which have a plus sign , in one 
column, and all the products ivhicli have a minus sign, in an¬ 
other. 

III. Add up the columns separately and take the difference 
of their sums: this difference will be double the area of the land. 












116 


ELEMENTS OF SURVEYING. [BOOK II 


30. We will now make the calculations in numbers. 
Having balanced the work, we can place it in the follow 
ing table. I ~ ' , 



Sta. 

Bearings. 

Dist. 

Dif. Lat. 

Dep. 

D. M. I>. 

Area. 

+ 

Area. 


1 

N 31|° W 

10. 

+ 8.71 

— 5.24 

+ 5.24 

45.6404 


I 

2* 

N 62|° E 

9.25 

+ 4.40 

+ 8.21 

+ 8.21 

36.1240 


'V- 

3 

S 36° E 

7.60 

— 6.01 

+ 4.46 

+ 20.88 


125.4888 

$ 

4 

8 45*° W 

10.40 

— 7.10 

— 7.43 

+17.91 


127.1610 








81.7644 

252.6498 


81.7644 

2)170.8854 

Area in square chains .... 85.4427 

Dividing by 10 . 8.54427 

4 

2.17708 

40 

•tfns. 8 j3. 2 R. 7 P. ..... 7.08320 

Observing in the field notes that station 2 is the most 
westerly point of the land, we assume the meridian which 
passes through this point, as the one from which the me¬ 
ridian distances are to be calculated. We mark the prin¬ 
cipal station with a star. 

Opposite station 2, we enter, in the column of double 
meridian distances, headed D. M. D., the departure of the 
course from 2 to 3, which is the double meridian distance 
of that course, and plus. To this we add the departure 
of the course, and also the departure of the next course r 
their sum is the double meridian distance of the course 
from 3 to 4. 

To the last sum add the departure opposite station 3, 
and the minus departure opposite station 4: their algebraic 
sum is the double meridian distance from 4 to 1. 

To the last sum add the last departure, which is minus, 
also the next departure which is likewise minus: this will 
give the double meridian distance of the course from 1 to 
2, which is equal to its departure. 

Then forming the products, adding them together, ta¬ 
king their difference, and dividing it by 2, according to 
the rule, we obtain the contents of the ground. 




























SEC. Ill] 


OF PLOTTING. 


117 


OF PLOTTING. 


31. It only remains to make 
a plot of the ground. 

For this purpose, draw any 
line, as NS, to represent the me¬ 
ridian passing through the princi¬ 
pal station; and on this line take 
any point, as 3, to represent that 
station. 


N 



FIRST METHOD. 

Having fixed upon the scale on which the plot is to be 
made, lay off from 3 on the meridian, a distance Bs equal 
to the difference of latitude of the first course, and at s 
erect a perpendicular to the meridian, and make it equal 
to the departure of the first course: then draw BC, which 
will be the first course. 

Through C draw a meridian, and make Cf equal to the 
difference of latitude of the second course, and through / 
draw a perpendicular fD , and make it equal to the depar¬ 
ture of the second course: draw CD, and it will bs the 
second course. 

Lay down, in the same manner, the courses DA and 
AB \ and the entire plot will be completed. 

SECOND METHOD. 

The work may be plotted in another manner, thus. 
At the principal station B ’ lay off an angle equal to the 
bearing from B to C, which will give the direction of BC. 
Then, from the scale of equal parts, make BC equal to the 
first course, this will give the station C. 

Through C draw a meridian, and lay off an angle equal 
to the bearing from C to D , and then lay off the course 
CD. Do the same for the bearing at D and the course 
DA ; also, for the bearing at A and the course AB, and a 








118 


ELEMENTS OF SURVEYING. [BOOK II 


complete plot of the ground will thus be obtained. If the 
work is all right, the last line AB will exactly close the 
figure. This plot is made on a scale of 10 chains to an inch. 

1, It is required to determine the contents and plot of a 
piece of land, of which the following are the field notes, viz. 


Stations. 

Bearings. 

Distances. 

1 

N 46J° W 

20 ch. 

2 

N 51}° E 

13.80 

3 

E 

21.25 

4 

S 56° E 

27.60 

5 

S 33i° W 

18.80 

6 

N 74i° W 

30.95 


CALCULATION. 


Sta¬ 
ll ous 

Bearings. 

Dis. 

Dif. 

Lat. 

Dep. 

BALANCED. 

D.M.D. 

+ 

AREA. 

+ 

AREA. 

N 

+ 

s 

E 

+ 

W 

Lat. 

Dep. 

1 

N 46i° W 

20 ch 

13.77 



14.51 

+13.88 

—14.56 

14.56 

202.0928 


o# 

N 51$° E 

13.80 

8.54 


10.84 


+8.61 

+10-81 

10.81 

93.0741 


3 

E 

21.25 



21.25 



+21.20 

42.82 



4 

S 56° E 

27.60 


15.44 

£2.88 


—15.29 

+22.82 

86.84 


1327.7836 

5 

S 33}° W 

18.80 


15.72 


10.31 

—15.63 

—10.36 

99.30 


1552.0596 

6 

N 74io w 

30.95 

8.27 



29.83 

+8.43 

—29.91 

59.03 

497.6229 


Sum of courses 132.40 

30.58 

31.16 

54.97 

54.65 




792.7898 

2879.8426 


Error in northing .. 0.58 


0.32 


Error in Westing 
Jins. 104 A 1R 16 P 


792.789* 
2)2087.0528 
. 1043.5264 


Plot of the example. 



V 



















































SEC. I XL] 


PROBLEMS. 


119 


32. Remark. When a bearing is due east or west, the 
error in latitude is nothing; the course must then be sub¬ 
tracted from the sum of the courses, and the remainder 
taken in balancing the columns of latitude. In the last 
example, the 3d bearing is due east, and the first term of 
the several proportions for error in latitude, was 132.40 — 
21.25 = 111.15. 

In like manner, if a bearing is due north or south, the 
error in departure is nothing; and the sum of the courses 
must be diminished by this course, before balancing the 
columns of departure. 

2. Required the contents, and plot of a piece of land, 
of which the following are the field notes. 


Stations. 

Bearings. 

Distances. 

1 

S 34° W 

3.95 ch. 

2 

S 

4.60 

3 

S 36i° E 

8.14 

4 

N 59i° E 

3.72 

5 

N 25° E 

6.24 

6 

N16° W 

3.50 

7 

N65° W 

8.20 


Arts, 10A. OB. 5P. 


3. Required the contents - and plot of a piece of land, 
from the following field notes. 


Stations. 

Bearings. 

■ ■ 1 - ■■■■■-■■■.. " 

Distances. 

1 

S 40° W 

70 rods 

2 

1ST 45° W 

89 

3 

N 36° E 

125 

4 

1ST 

54 

5 

S 81° E 

186 

6 

S 8°W 

137 

7 

W 

130 


Ans. 207.4. SR. 33 P. 














120 


ELEMENTS OF SURVEYING. [BOOK II 


4. Required the contents and plot of a piece of land, 
from tlie following field notes. 


Stations. 

Bearings. 

Distances. 

1 

in 

O 

o 

31.80 ch. 

2 

N 54° E 

2.08 

3 

1ST 29i° E 

2.21 

4 

N28f° E 

35.35 

5 

N57° W 

21.10 

6 

S 47° W 

31.30 


Am. 92 A. 3 R. 32 P. 


5. Required the area of a survey of which the follow 
ing are the field notes. 


Stations. 

Bearings. 

Distances. 

1 

N 42° E 

5.00 ch. 

2 

East. 

4.00 

3 

K9 C E 

4.00 

4 

S 69° E 

5.56 

5 

S 36° E 

7.00 

0 

S 42° W 

4.00 

7 

S 75° W 

10.00 

8 

N 39° W 

7.50 


If, in this example, we assume 1 as the principal sta 
tion, the double meridian distances will all be plus, and 
the positive area will exceed the negative. 

In balancing we shall find the error in southing to be 
.28 ch. and in westing .22 ch. The area is 13 A. OR. IIP. 
It should however be remarked, that in all* the examples 
the answers may be slightly varied by distributing the 
corrections. 

6. What is the area of a survey of which the following 
are the field notes. 














SEC. IIL] 


PROBLEMS 


121 


Stations. 

Bearings. 

Distances. 

1 

N 75° 00' E 

54.8 rods. 

2 

N 20° 30' E 

41.2 

3 

East. 

64.8 

4 

S 83° 30' W 

141.2 

5 

S 76° 00' W 

64.0 

6 

North. 

36.0 

7 

S 84° 00' W 

46.4 

8 

N 53° 15' W 

46.4 

9 

N 36° 45' E 

76.8 

10 

N 22° 30' E 

56.0 

11 

S 76° 45' E 

48.0 

12 

S 15° 00' W 

43.4 

13 

S 16° 45' W 

40.5 


In this survey 4 is the most easterly and 9 the most 
westerly station. The area is equal to llOA 2 R. 23 P. 
It may vary a little, on account of the way in which the 
balancing is done. 

7. What are the contents of a piece of land of which 
the following are the field notes? 


Stations. 

Bearings. 

Distances. 

1 

S 75° W 

13.70 ch. 

2 

S 20i° W 

10.30 

3 

West. 

16.20 

4 

N 33i° e 

35.30 

5 

N 76° E 

16.00 

6 

South. 

9.00 

7 

N 84° E 

11.60 

8 

S 531° E 

11.60 

9 

S 36f° W 

19.20 

10 

S 221° w 

14.00 

11 

N 76J° w 

12.00 

12 

N 15° E 

10.85 

13 

N 16|° E 

10.12 


















122 


ELEMENTS OF SURVEYING [BOOK II 


In this survey 4 is the^most westerly station and 9 the 
most easterly. The area is 110 A. 2 B. 23 P. The result 
may, however, as in the other examples, be slightly varied 
by the balancing. 

8. What is the area of a survey of which the following 
ore the notes? 


Stations. 

Bearings. 

Distances. 

1 

S 46£° E 

80 rods 

2 

S 51f° W 

55.20 

3 

West. 

85 

4 

N 56° W 

110.40 

5 

N 33i° E 

75.20 

6 

S 74J° E 

123.80 


Ans 104A IB. UP. 


I. To determine the contents and boundary of a piece of land , 
by means of offsets from the principal lines. 

33. An offset is a line measured perpendicular to a 
course, and may lie either on the right or left of it. 

Let ABODE be a piece of 
ground to be surveyed. Let us 
suppose it to be bounded on the 
west and north by a fence and 
road, and on the east and south 
by a creek or river. 

Assume as stations the prin¬ 
cipal points A, A, (7, Z>, and E. 

Take, with the compass, the bear¬ 
ings from A to B, from B to C ) 
from 0 to A, from D to E\ and 
from E to A ; and measure the dis¬ 
tances AB, BC 1 CD , DE\ and EA. 

At convenient points of the course AB, as a, c, and /J 
measure the oflsets ah, cd , fg. Then, having measured 
these .:nes, as also the distances Aa, ac , cf and fB, enough 














SEC. III.] 


PROBLEMS. 


123 


will be known to determine the area wliicli lies without the 
station line AB. The points b , cl and g , of the fence which 
runs from A to B, are also determined. 

Erect, in a similar manner, offsets to the other courses, 
and determine the areas which lie without the station lines. 
These several areas being added to the area within the 
station lines, will give the entire area of the ground. 

If the offsets fall within the station lines, the corres¬ 
ponding area must be subtracted from the area which is 
bounded by the station lines. 

II. To determine the bearing and distance from one point to 
another, when the points are so situated that one cannot be 
seen from the other. 

34. Let A and 0 be the two 
points, and AB a meridian pass¬ 
ing through one of them. From 
either of them, as A, measure a 
course .42, of a convenient length 
in the direction towards C, and 
take the bearing with the com¬ 
pass. At 2, take the bearing of 
a second course, and measure the 
distance to 3. At 3, take a third 
bearing and measure to 4. At 
4, take the bearing to 0, and 
measure the distance from 4 to C. 

Then, the difference between the sum of the northings 
and the sum of the southings will be represented by AB, 
and the difference between the sum of the eastings and 
the sum of the westings by BC. The base AB , and the 
perpendicular BG of the right-angled triangle ABC, are then 
known. The angle at the base, BAC, is the bearing from 
A to O; or the equal alternate angle at C is the bearing 
from C to A, and the hypothenuse A C is the distance. 

35. Having measured the bearings and courses on the 
field, form a table, and find the base and perpendicular 
of the right-angled triangle, in numlers. 






124 


ELEMENTS OF SURVEYING. [BOOK II 


Stations. 

Bearings. 

- 4. - 

Distances. 

N. 

s. 

E. 

w. 

1 

H61° W 

40 ch 

19.39 



34.98 

2 

H 42° W 

41. 

30.47 



27.43 

3 

1ST 12° E 

16.10 

15.75 


3.35 


4 

1ST 47° E 

32.50 

22.16 


23.77 




AB 

= 87.77 


27.12 

62.41 


27.12 



CB- 35.29 ch 


C r > 

B 

Remark. Had any of the 


i 

1 

courses run south, AB would have / 


1 

1 

been equal to the sum of the A / 


i 

i 

i 

northings, minus the sum of the / 


i 

i 

i 

southings. A 


i 

i 

i 

To find the angle BA C, or the \ 


i 

i 

i 

bearing from A to C. 


i 

i 

i 

As radius : tan A : : AB : BC ) 

\ 

1 

i 

V | 

or AB : BC : : B : tan A : 


V'! 

\ • 

that is, 


d\: 

A 

As AB 87.77 . ar. comp. 

8.056654 


: BC 35.29 . 

1.547652 


• • R 

• • JL 4/ • • • • « # 

10. 


• tan A 21° 54' 12" 

9.604306 


To find the distance AC. 



As sin A 21° 54' 12" ar. comp. 

0.428242 


• ^ t •••••• 

10. 


: : BC 35.29 .... 

1.547652 


: AC 94.6 .... 

1.975894 



Hence, the bearing and distance are both found. 


OF SUPPLYING OMISSIONS IN THE FIELD NOTES. 

36. The last problem affords an easy method of finding 
the bearing and length of one of the courses of a survey 
































8EC. Ill] 


PROBLEMS. 


125 


when the bearings and lengths of all the others are known. 
It may be necessary to nse this method when there are 
obstacles which prevent the measuring of a course, or when 
the bearing cannot be taken. Indeed, two omissions may 
in general be supplied by calculation. It is far better, 
however, if possible, to take all the notes on the field. 
For, when any of them are supplied by calculation, there 
are no tests by which the accuracy of the work can be as¬ 
certained, and all the errors of the notes affect also the 
parts which are supplied. 


1. In a survey we have the following notes: 


Stations. 

Bearings. 

Distances. 

1 

1ST 31J° W 

10 ch. 

2 

N 62f° E 

9.25 

3 

Lost. 

Lost. 

4 

S 45i° W 

10.40 


What is the bearing and distance from station 3 to 4 ? 

A (Bearing, S 38° 52' E. 

( Distance, 7.03 ch. 


2. In a survey we have the following notes: 


Stations. 

Bearings. 

Distances. 

1 

S 40J° E 

31.80 ch. 

2 

N54° E 

2.08 

3 

Lost. 

Lost. 

4 

o 

«|-* 

oo 

CM 

35.35 

5 

1ST 57° W • 

21.10 

6 

_ 

S 47° W 

31.30 


What is the bearing and distance from 3 to 4? 

m j Bearing, N 34° 47' E. 
nS ' ' Distance, 2.19 ch. 


















126 ELEMENTS OF SURVEYING. [BOOK H 

III. To determine the angle included between any two courses , 

when their bearings are known. 

N 

37. Let NS be a meridian 
passing through A. 

Let AB , AO, AH, AD, and 
AF\ be five courses running 
from A. We readily deduce 
the following 

S 



PRINCIPLES. 


AC is N 26° W 
AH is N 65° W 

CAH= 39° 


When the meridional letters 
are alike, and those of depar 
ture also alike, the difference oj 
the bearings is the angle between 
the courses. 


AB is N 46° E 
AC is N 26° W 

CAB = 72° 


AC is N 26° W 
AD is S 66° W 

£10 = 180°- 92°= 88° 


AC is N 26 c W 
AF is S 66° E 

CAF= 180°-40°= 140° 


When the meridional letters 
are alike, and those of depar¬ 
ture unlike, the sum of the bear¬ 
ings is the angle between the 
courses. 

When the meridional letters 
are unlike, and those of depar¬ 
ture alike, the angle between the 
courses is equal to 180°, minus 
the sum of the bearings. 

When the meridional letters 
are unlike, and those of depar¬ 
ture also unlike, the angle be¬ 
tween the courses is equal to the 
difference of the bearings taken 
from 180°. 


Remark. The above principles are determined, under the 
supposition that the two courses are both run from the 
angular point Hence, if it be required to apply them to 








SEC. Ill] 


OF DIVIDING LAND. 


127 


two courses roi in the ordinary way, as we go around the 
field, the bearing of one of them must be reversed before 
the calculation for the angle is made. 

1. The bearings of two courses, from the same point, 
are FT 37° E, and S 85° W: what is the angle included 
between them? 

Ans. 132°. 

2. The bearings of two adjacent courses, in going round 
a piece of land, are 1ST 39° W, and S 48° W: what is the 
angle included between them? 

Ans. 87°. 

3. The bearings of two adjacent courses, in going round 
a piece of land, are S 85° W, and 1ST 69° W: what is the 
angle included between them? 

Ans. 154°. 

4. The bearings of two adjacent courses, in going round 
a piece of land, are N 55° 30' E, and S 69° 20' E : whai 
is the angle included between them? 

Ans. 124° 50'. 

OF DIVIDING LAND. 

38. Fields are so variously shaped that it is difficult 
to give rules that will apply to all cases. It is by practice 
alone that facility is obtained in that branch of survey¬ 
ing relating to the division of estates. We shall add only 
a few examples that may serve as general guides in the 
application of the principles of Plane Geometry to such 
cases as may arise. 

T. To run a line from the vertex of a triangular field which 

shall divide it into two parts, having to each ether the 

ratio of M to N. 

39. Let ABC be any triangular field. 

Divide the side BC into two 

parts, such that (Geom., Bk. IV., 

Prob. 1.) 

BD : DC :: m : 
and draw the line AD: 

then will, ABD • DAC : : m : n. 


A 






128 


ELEMENTS OF SURVEYING. [BOOK IL 


For, the two triangles ABD , ADO haying the same alti¬ 
tude are to each other as their bases (Geom., Bk. IV., P. 6, 
C.): hence, the triangle is divided into parts haying the 
ratio of m to n. 


II. To run a line parallel to one side of a triangular field, 
that shall form with the parts of the two other sides a 

triangle equivalent to the —part of the field. 

40. Let CBA represent a triangular field and CA the 
side parallel to which the dividing line is to be drawn. 


On the side BO describe 
a semicircle : then divide BC 
at D , so that 

BD : BO : : m : n. 


At D, erect th) perpendicular DG to the diameter BC, 
and draw BG. Then, with A as a centre, and BG as a 
radius, describe the arc of a circle cutting BO at M 
Through E draw EF parallel to CA, and it will divide the 
triangle in the required ratio. 

For, (Geom., Bk. IV., P. 23.) 

M' = BOX BD : 



or. 


—o —o BD 
BE 2 = BC~ X gQ 5 whence, 


BE~ : BC~ : : BD : BO : : m : n. 
But, since the triangles BEF\ BOA are similar, 

BE- : BG 2 : : BEF : BOA. 
Wherefore, from equality of ratios, 

BEF : BOA : : m 


n ; 


and 


m 

BEF=—xBOA. 


Remark. The points E and F may easily be found 
by computation. 


For, since BE' = BOxBD, and BD = ~xBC 

n 1 












SEC. IIL’| 


OF DIVIDING LAND. 


129 


we have 


BE 2 = BO*X~] or BE=BC 



Tn. like manner 


BF=BA 



EXAMPLE. 


Let it be required to divide the trian¬ 
gular field CAB, in which AC =9 ch. AB — 
11 ch. and CB — 7 ch. into two such parts 
that ABE shall be one-fourth of the whole 
field. 

In this case, we have 


m = 1. n = 4, and — = 

n 



m 



i 


1 

2 



hence, 


AE= 4 ch. 50 1. and AB = 5 ch. 50 1. 


III. To run a line from a given point in the boundary of a 
piece of land, so as to cut off, on either side of the line , 
a given portion of the field. 

41. Make a complete survey of the field, by the rules 
already given. Let us take, as an example, the field whose 
area is computed at page 118. That field contains 1044 
IB )6Pj and the following is a plot of it. 



Let it now be required to run a line from station A , 
in such a manner as to cut off on the left any part of the 

field; say, 2 6A 2 B 3IP. 

9 







ISO ELEMENTS OF SURVEYING [ROOK U 

It is seen, by examining tlie field, that the division line 
will probably terminate on the course CD. Therefore, draw 
a line from A to C, which we will call the first closing 
line. 

The bearings and lengths of the courses AB, BC 1 are 
always known; and in the present example are found in 
the table on page 118: hence, the bearing and distance 
from C to A, can be calculated by Art. 35: they are in 
this example, 

Bearing S 9° 28' E : Course 22.8 ch. 

Having calculated the bearing and length of the closing 
line, find, by the general method, the area which it cuts 
off: that area, in the present case, is 

ISA SR SR 

It is now evident that the division line must fall on 
the right of the closing line AC, and must cut off an area 
ACH , equal to the difference between that already cut off, 
and the given area: that is, an area equal 

2 6A 2 R 31 P given area, 

13A SR 3 P area already cut off, 

to . . . 12A SR 28 P. 

Since the bearing of the next course CD, and the bear¬ 
ing of the closing line AC are known, the angle A CD 
which they form with each other, can be calculated, and is 
in this example 80° 32°. Hence, knowing the hypothenuse 
AC, and the angle ACC at the base, the length AC of 
the perpendicular let fall on the course CD, can be found, 
and is 22.49 chains. 

Since the area of a triangle is equal to its base multi¬ 
plied by half its altitude, it follows, that the base is equal 
to the area divided by half the altitude. Therefore, if the 
area 

12A SR 28 P 

be reduced to square chains, and divided by 11.24J chains, 
which is half the perpendicular A C, the quotient, which is 
11.58 chains, will be the base CH. Hence, if we lay off 
from C, on CD , a distance CH, equal to 11.58 clains, and 




EEC. IV.] 


PUBLIC LANDS. 


131 


then run the line AH, it will cut off from the land the re¬ 
quired area. 

Remark I. If the part cut off by the first closing line, 
should exceed the given area, the division line will fall on 
the left of AC. 

Remark II. If the difference between the given 
area and the first area cut off, divided by half the per¬ 
pendicular AC, gives a quotient larger than the course 
CD; then, draw a line from A to D, and consider it as 
the first closing line, and let fall a perpendicular on DE. 

Remark IIL When the point from which the divi¬ 
sion line is to be drawn, falls between the extremities 
of a course, dividing the course into two parts, con¬ 
sider one of the parts as an entire course, and the other 
as forming a new course, having the same bearing. The 
manner of making the calculation will then be the same 
as before. 



SECTION IV. 


PUBLIC LANDS—VARIATION OF THE NEEDLE. 

1. Soon after the organization of the present govern 
ment, several of the states ceded to the United States large 
tracts of wild land, and these, together with the lands since 
acquired by treaty and purchase, constitute what is called 
the public lands, or public domain. Previous to the year 
1802, these lands were parcelled out without reference to 
any general plan, in consequence of which the titles often 
conflicted with each other, and in many cases, several grants 
covered the same premises. 

In the year 1802, the following method of surveying 
the public lands, was adopted by Colonel Jared Mansfield, 
then surveyor-general of the North-Western Territory. 

2. The country to be surveyed is first divided by 
meridians, six miles distance from each other; and then 




132 ELEMENTS OF SURVEYING. [BOOK 11 

again, by a system of east and west lines, also six miles 
from each other. The country is thus divided into equal 
squares, which are called townships. Hence, each township 
is a square, six miles on a side, and contains thirty-six 
square miles. 

3. For the purpose of illustration, we have obtained 
from the general land office the accompanying map, which 
represents a considerable portion of the State of Arkansas 

The principal meridian in this Survey is called the 5th 
meridian, and passes through the point of junction of the 
White river and the Mississippi. The principal base line, 
running east and west, intersects this meridian a little to the 
east of White river; and from the meridian and base line, 
reckoned from this point of intersection, all the ranges of 
townships are laid off. 

For example, 1 North, will apply to all the townships 
lying in the first row north of the base line: 1 South, will 
apply to all the townships in the first row south of the base¬ 
line. Range 1 East, will apply to all the townships lying 
in the first row, east of the 5th meridian : and range 1 
West, will apply to all lying in the first row to the west 
of it. The small figures designate the rows of townships, 
reckoned north and south from the base line, and the 
ranges reckoned east and west from the 5th meridian. 
Thus, township 1 North, range 4 West, has its exact place 
designated, and may be immediately located. 

4. The principal meridians, and the principal base lines 
are established by astronomical observation, and the lines 
of subdivision run with the compass. 

For convenience in making surveys, and for the purpose 
of designating particular localities, a state or large tract, is 
often divided into parts called “ Districts.” There are three 
such districts in the map before us, the boundaries of which 
are designated by the full dark lines. 

5. Each township is divided into equal squares, by me¬ 
ridians one mile apart, and by east ana west lines at the 
same distance from each other. Hence, each township is 
divided into 36 square miles, each one of which is called 


















































































































































































































































































































134 


ELEMENTS OF SURVEYING. [BOOK IL 


a section . The sections of a township are numbered from 
1 to 36, beginning at the north-east angle, and each con* 
tains 640 acres 

The diagram exhibits the 36 sections of a township. 


\ 


6 

5 

4 

3 

2 

— 

1 - 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

. 27 

26 

25 

31 

32 

33 

34 

35 

36 


To describe a section accurately, we say, section num¬ 
ber 5, in township number 4 north, in range 3d west of a 
known meridian; the one, for example, drawn through the 
mouth of White river. The description fixes precisely the 
place of the section. Go to the 3d range of townships, 
west of the known meridian, find township number 4 north, 
in this range, and lastly, section number 5 of that town¬ 
ship. The corners of the sections should be marked by 
permanent corner-posts, or by lines blazed on trees. 

6. The sections are divided into half sections, quarter 
sections, and even into eighths of sections. ( The following 
table shows the contents of a township, and its subdivi¬ 
sions : 

1 township = 36 sections = 23040 acres. 

1 section = 640 acres. 

\ section = 320 acres. 

{ section = 160 acres. 

•| section = 80 acres. 
















SEC. IV.] VARIATION OF THE NEEDLE. 


135 


VARIATION OF THE NEEDLE. 

7. Tlie angle which the magnetic meridian makes with 
the true meridian, at any place on the surface of the earth, 
is called the variation of the needle at that place, and is east > 
or west, according as the north end of the needle lies on 
the east or west side of the true meridian. 

8. The variation is different at different places, and 
even at the same place it does not remain constant for any 
length of time. The variation is ascertained by comparing 
the magnetic, with the true meridian. 

9. If we suppose a line to be traced through those 
points on the surface of the earth, where the needle points 
directly north, such a line is called the line of no variation. 
At all places lying on the east of this line, the variation 
of the needle is west; at all places lying on the west of 
it, the variation is east. 

10. The public is much indebted to Professor Loomis, 
for the valuable results of many observations and much 
scientific research, on the dip and variation of the needle, 
contained in the 39th and 42d volumes of Silliman’s 
Journal. 

The variation at each place was ascertained for the year 
1840 ; and by a comparison of previous observations and 
the application of known formulas, the annual motion, or 
change in variation, at each place, was also ascertained, and 
both are contained in the tables which follow. 

11. If the annual motion was correctly found, and con¬ 
tinues uniform, the variation at any subsequent period can 
be ascertained by simply multiplying the annual motion 
bv the number of years, and adding the product, in the 
algebraic sense, to the variation in 1840. It will be ob¬ 
served that all variations west are designated by the plus 
sign ; and all variations east, by the minus sign. The an¬ 
nual motions being all west, have all the plus sign. 


136 ELEMENTS OF SURVEYING. [BOOK II 

12. Our first object will be to mark the line, as it was 
in 1840, of no variation. For this purpose we shall make 
a table of places lying near this line. 


PLACES NEAR THE LINE OF NO VARIATION. 


Place. 

Latitude. 

Long 

'itude. 

Variation. 

An. Motion. 

A Point. 

o 

O 

53' 

O 

O 

OO 

13' 

0° 

00' 

+ 4'.4 

Cleveland, O. 

41 

31 

81 

45 

-0 

19 

4.4 

Detroit, Mich. 

42 

24 

82 

58 

-1 

56 

4 

Mackinaw. 

45 

51 

84 

41 

-2 

08 

3.9 

Marietta, O. 

39 

30 

81 

28 

-1 

24 

4.3 

Charlottesville, V a. 

39 

02 

78 

30 

-f* 0 

19 

3.7 

Charleston, S. C. 

32 

42 

80 

04 

-2 

44 

1.3 


At the point whose latitude is 40° 53', longitude 80° 
13', the variation of the needle was nothing in the year 
1840, and the direction of the line of no variation, traced 
north, was hi 24° 35' west. The line of no variation, pro¬ 
longed, passed a little to the east at Cleveland, in Ohio— 
the variation there being 19 minutes east. Detroit lay still 
further to the west of this line, the variation there being 
1° 56' east; and Mackinaw still further to the west, as 
the variation at that place was 2° 08' east. 

The course of the line of no variation, prolonged south¬ 
erly, was S 24° 35' E. Marietta, in Ohio, was west of this 
line—the variation there being 1° 24' east. Charlottesville, 
in Virginia, was a little to the east of it—the variation there 
being 19' west; whilst Charleston, in South Carolina, was on 
the west,—the variation there being 2° 44’ east. 

From these results, it will be easy to see aboui where 
the line of no variation is traced in our own country. 

13. We shall give two additional tables: 
















SEC. IV.] VARIATION OF THE NEEDLE. 


137 


PLACES WHERE THE VARIATION WAS WEST. 


— 

Places. 

Latitude. 

Longitude. 

V ariation. 

An. Motion. 

Angle of Maine. 

OO 

o 

00' 

67° 

37' 

+ 19° 

30' 

+ 8'. 8 

Waterville, Me. 

44 

27 

69 

32 

12 

36 

5.7 

Montreal. 

45 

31 

73 

35 

10 

18 

5.7 

Keesville, 1ST. Y. 

44 

28 

73 

32 

8 

51 

5.3 

Burlington, Yt. 

44 

27 

73 

10 

9 

27 

5.3 

Hanover, 1ST. H. 

43 

42 

72 

14 

9 

20 

5.2 

Cambridge, Mass. 

42 

22 

71 

08 

9 

12 

5 

Hartford, Ct. 

41 

46 

72 

41 

6 

58 

5 

Newport, R. I. 

41 

28 

71 

21 

7 

45 

5 

Geneva, N. Y. 

42 

52 

77 

03 

4 

18 

4.1 

West Point. 

41 

25 

74 

00 

6 

52 

4 

New York City. 

40 

43 

71 

01 

5 

34 

3.6 

Philadelphia. 

39 

57 

75 

11 

4 

08 

3.2 

Buffalo, N. Y. 

42 

52 

79 

06 

1 

37 

4.1 


PLACES WHERE THE VARIATION WAS EAST. 


Places. 

Latitude. 

Longitude. 

Variation. 

An. Motion. 

Mouth of Colum- j 







Unknown. 

bia River. ) 

46° 

12' 

123° 

30' 

-21° 

40' 

Jacksonville, HI. 

39 

43 

90 

20 

8 

28 

+ 2'.5 

St. Louis, Mo. 

38 

37 

90 

17 

8 

37 

2.3 

Nashville, Tenn. 

36 

10 

86 

52 

6 

42 

2 

Louisiana, at 

29 

40 

94 

00 

8 

41 

1.4 

Mobile, Ala. 

30 

42 

88 

16 

7 

05 

1.4 

Tuscaloosa, Ala. 

33 

12 

87 

43 

7 

26 

1.6 

'Columbus, Geo. 

32 

28 

85 

11 

0 

28 

2 

Milledgeville, u 

33 

07 

83 

24 

5 

07 

2.4 

Savannah, 

32 

05 

81 

12 

4 

13 

2.7 

Tallahassee, FI. 

30 

26 

84 

27 

5 

03 

1.8 

Pensacola, 11 

30 

24 

87 

23 

5 

53 

1.4 

Logansport, Ind. 

40 

45 

86 

22 

5 

24 

2.7 

iCincinnati, O. 
i —-- 

39 

06 

84 

27 

4 

46 

3.1 



































138 


ELEMENTS OF SURVEYING. [BOOK II 


METHODS OF ASCERTAINING THE VARIATION. 

* 

14. The best practical method of determining the true 
meridian of a place, is by observing the north star. If this 
star were precisely at the point in which the axis of the 
earth, prolonged, pierces the heavens, then, the intersection 
of the vertical plane passing through it and the place, with 
the surface of the earth, would be the true meridian. But, 
the star being at a distance from the pole, equal to 1° 3T 
nearly, it performs a revolution about the pole in a circle, 
the polar distance of which is 1° 30': the time of revo¬ 
lution is 23 h. and 56 min. 

To the eye of an observer, this star is continually in 
motion, and is due north but twice in 23 h. 56 min.; and 
is then said to be on the meridian. Now, when it departs 
from the meridian, it apparently moves east or west, for 5 
h. and 59 min., and then returns to the meridian again. 
When at its greatest distance from the meridian, east or west, 
it is said to be at its greatest eastern or ivestern elongation. 

The following tables show the times of its greatest 
eastern and western elongations : 

EASTERN ELONGATIONS. 


Days. 

April. 

May. 

June. 

July. 

August. 

Sept. 


H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

1 

18 

18 

16 

26 

14 

24 

12 

20 

10 

16 

8 

20 

7 

17 

56 

16 

03 

14 

00 

11 

55 

9 

53 

7 

58 

13 

17 

34 

15 

40 

13 

35 

11 

31 

9 

30 

7 

36 

19 

17 

12 

15 

17 

13 

10 

11 

07 

9 

08 

7 

15 

25 

16 

49 

14 

53 

12 

45 

10 

43 

8 

45 

6 

53 


WESTERN ELONGATIONS. 


Days. 

Oct. 

Nov. 

Dec. 

Jan. 

Feb. 

March. 


H. M. 

H. M. 

H. M. 

H. M. 

H. 

M. 

H. 

M. 

1 

18 18 

16 22 

14 19 

12 02 

9 

50 

8 

01 

7 

17 56 

15 59 

13 53 

11 36 

9 

26 

7 

38 

13 

17 34 

15 35 

13 27 

11 10 

9 

02 

7 

16 

19 

17 12 

15 10 

13 00 

10 44 

8 

39 

6 

54 

25 

16 49 

14 45 

12 34 

10 18 

8 

16 

6 

33 

. 































SEC. IV.J YARIATION OF THE NEEDLE. 


139 


The eastern elongations are put down from the first 
of April to the first of October; and the western, from the 
first of October to the first of April; the time is computed 
from 12 at noon. The western elongations in the first case, 
and the eastern in the second, occurring in the daytime, 
cannot be used. Some of those put down are also invisi¬ 
ble, occurring in the evening, before it is dark, or after day¬ 
light in the morning. In such case, if it be necessary to de¬ 
termine the meridian at that particular season of the year, 
let 5 h. and 59 min. be added to, or subtracted from, the time 
of greatest eastern or western elongation, and the observ¬ 
ation be made at night, when the star is on the meridian. 

15. The following table exhibits the angle which the me¬ 
ridian plane makes with the vertical plane passing through 
the pole-star, when at its greatest eastern or western elon¬ 
gation : such angle is called the azimuth. The mean angle 
only is put down, being calculated for the first of July of 
each year: 

AZIMUTH TABLE. 


Year. 

Lat. 32° 

Azimuth. 

Lat. 34° 

Azimuth. 

Lat. 36° 

Azimuth. 

Lat. 38° 

Azimuth. 

Lat. 40° 

Azimuth. 

Lat. 42° 

Azimuth. 

Lat. 44° 

Azimuth. 

1851 

1° 45J' 

1° 48' 

1° 50}' 

1° 53 *-' 

1° 56|' 

2° 00-p 

2° 04}' 

1852 

1° 45' 

1° 47*' 

1° 50' 

1° 53' 

1° 56}' 

1° 59?' 

2° 03f 

1853 

1° 44}' 

1° 47' 

1° 49f' 

1° 52}' 

1° 55J' 

1° 59}' 

2° 03i' 

1854 

1° 44}' 

1° 46}' 

1° 49}' 

1° 52' 

1° 55}' 

1° 59' 

2° 02f' 

1855 

r 48?' 

1° 46-ip 

1° 48f' 

1° 51f' 

1° 54f' 

1° 58}’ 

2° 02}' 

1856 

*«*. 

rH[^f 

CO 

o 

t-H 

1° 45f' 

1° 48}' 

1° 51}' 

1° 54?' 

1° 58' 

2° Olf 

1857 

1° 43' 

1° 45p' 

1° 48' 

1° 50f' 

1° 54' 

1° 57?' 

2° 01?' 

1858 

1° 42?' 

1° 44J' 

r 47j 

1° 50?' 

1° 53}' 

1° 57' 

2° 00|' 

1859 

1° 42' 

1° 44}' 

1° 47' 

1° 49?' 

1° 53' 

1° 56?'- 

2° 00*'“ 

1860 

1° 41?' 

1° 44' 

1° 46?' 

1° 494' 

1° 52*' 

1° 56' 

2° 00' 

1861 

1° 41}' 

i 

1° 48?' 

1° 46p 

l c 49' 

!'■ 52?' 

1° 55‘i' 

i ° »»! 































































































































140 


ELEMENTS OF SURVEYING. [BOOR II 


The use of the above tables, in finding the true meri¬ 
dian, will soon appear. 

TO FIND THE TRUE MERIDIAN WITH THE THEODOLITE. 

16. Take a board, of about one foot square, paste white 
paper upon it, and perforate it through the centre; the 
diameter of the hole being somewhat larger than the diam¬ 
eter of the telescope of the theodolite. Let this board be 
so fixed to a vertical staff, as to slide up and down freely: 
and let a small piece of board, about three inches square, 
be nailed to the lower edge of it, for the purpose of hold¬ 
ing a candle. 

About twenty-five minutes before the time of the great¬ 
est eastern or western elongation of the pole-star, as shown 
by the tables of elongations, let the theodolite be placed 
at a convenient point and levelled. Let the board be 
placed about one foot in front of the theodolite, a lamp or 
candle placed on the shelf at its lower edge; and let the 
board be slipped up or down, until the pole-star can be 
seen through the hole. The light reflected from the paper 
will show the cross hairs in the telescope of the theodolite. 

Then, let the vertical spider’s line be brought exactly 
upon the pole-star, and, if it is an eastern elongation that 
is to be observed, and the star has not yet reached the 
most easterly point, it will move from the line towards the 
east, and the reverse when the elongation is west. 

At the time the star attains its greatest elongation, it 
will appear to coincide with the vertical spider’s line for 
some time, and then leave it, in the direction contrary to 
its former motion. 

As the star moves towards the point of greatest elonga 
tion, the telescope must be continually directed to it, by 
means of the tangent-screw of the vernier plate; and when 
the star has attained its greatest elongation, great care 
should be taken that the instrument be not afterwards 
moved. 

Now, if it be not convenient to leave the instrument in 
its place until daylight, let a staff, with a candle or small 


SEC. IV.J VARIATION OF THE NEEDLE. 141 

lamp upon its upper extremity, be arranged at thirty or 
forty yards from the theodolite, and in the same vertical 
plane with the axis of the telescope. This is easily effect* 
ed, by revolving the vertical limb about its horizontal axi 3 
without moving the vernier plate, and aligning the staff to 
coincide with the vertical hair. Then mark the point di¬ 
rectly under the theodolite; the line passing through this 
point and the staff, makes an angle with the true meridian 
equal to the azimuth of true pole-star. 

From the table of azimuths, take the azimuth corres¬ 
ponding to the year and nearest latitude. If the observed 
elongation was east, the true meridian lies on the west of 
the line which has been found, and makes with it an angle 
equal to the azimuth. If the elongation was west, the 
true meridian lies on the east of the line: and, in either 
case, laying off the azimuth angle with the theodolite, gives 
the true meridian. 

TO FIND THE TRUE MERIDIAN WITH THE COMPASS. 

17. 1. Drive two posts firmly into the ground, in a line 

nearly east and west; the uppermost ends, after the posts are 
driven, being about three feet above the surface, and the 
posts about four feet apart: then lay a plank, or piece of 
timber three or four inches in width, and smooth on the, 
upper side, upon the posts, and let it be pinned or nailed, 
to hold it firmly. 

2. Prepare a piece of board four or five inches square, 
and smooth on the under side. Let one of the compass- 
sights be placed at right angles to the upper surface of the 
board, and let a nail be driven through the board, so that 
it can be tacked to the timber resting on the posts. 

3. At about twelve feet from the stakes, and in the 
direction of the pole-star, let a plumb be suspended from 
the top of an inclined stake or pole. The top of the pole 
should be of such a height that the pole-star will appear 
about six inches below it; and the plumb should be swung 
in a vessel of water to prevent it from vibrating. 


142 


ELEMENTS OF SURVEYING 


[BOOK II 


This being done, about twenty minutes before the time 
of elongation, place the board, to which the compass-sight 
is fastened, on the horizontal plank, and slide it east 01 
west, until the aperture of the compass-sight, the plumb- 
line, and the star, are brought into the same range. Then 
if the star depart from the plumb-line, move the compass- 
sight, east or west, along the timber, as the case may be, 
until the star shall attain its greatest elongation, when it 
will continue behind the plumb-line for several minutes; 
and will then recede from it in the direction contrary to 
its motion before it became stationary. Let the compass- 
sight be now fastened to the horizontal plank. During this 
observation it will be necessary to have the plumb-line 
lighted: this may be done by an assistant holding a candle 
near it 

Let now a staff, with a candle or lamp upon it, be 
placed at a distance of thirty or forty yards from the 
plumb-line, and in the same direction with it and the com¬ 
pass-sight. The line so determined, makes, with the true 
meridian, an angle equal to the azimuth of the pole-star; 
and, from this line, the variation of the needle is readily 
determined, even without tracing the true meridian on the 
ground. 

Place the compass upon this line, turn the sights in the 
direction of it, and note the angle shown by the needle. 
Now, if the elongation, at the time of observation, was 
west, and the north end of the needle is on the west side of 
the line, the azimuth, plus the angle shown by the needle, 
is the true variation. But should the north end of the 
needle be found on the east side of the line, the elonga¬ 
tion being west, the difference between the azimuth and 
the angle would show the variation: and the reverse when 
the elongation is east. 

1. Elongation west, azimuth . . 2° 04' 

North end of the needle on the west, angle 4° 06' 

Variation 6° 10' west 


i 




BEC. IV.] VARIATION OF THE NEEDLE 148 

2. Elongation west, azimuth . . 1° 59' 

North end of the needle on the east, angle 4° 50' 

Variation 2° 51' east. 

8. Elongation east, azimuth . . 2° 05' 

North end of the needle on the west, angle 8° 80' 

Variation 6° 25' west. 

4. Elongation east, azimuth . . 1° 57' 

North end of the needle on the east, angle 8° 40' 

Variation 10° 87' east. 


Kemark I. The variation at West Point, in Septem* 
her, 1835, was 6° 82' west. 

Kemark II. The variation of the needle should al¬ 
ways be noted on every survey made with the compass, 
and then if the land be surveyed at a future time, the old 
lines can always be re-run. 

18. It has been found bv observation, that heat and 

i/ / 

cold sensibly affect the magnetic needle, and that the same 
needle will, at the same place, indicate different lines at 
different hours of the day. 

If the magnetic meridian be observed early in the 
morning, and again at different hours of the day, it will 
be found that the needle will continue to recede from the 
meridian as the day advances, until about the time of the 
highest temperature, when it will begin to return, and at 
evening will make the same line as in the morning. This 
change is called the diurnal variation , and varies, during 
the summer season, from one-fourth to one-fifth of a 
degree. 

19. A very near approximation to a true meridian, and 
consequently to the variation, may be had, by remember¬ 
ing that the pole-star very nearly reaches the true meri¬ 
dian, when it is in the same vertical plane with the star 
Alioth in the tail of the Great Bear, which lies nearest the 
four stars forming the quadrilateral. 








144 


ELEMENTS OF SURVEYING. [BOOK II 


The vertical position can be ascer¬ 
tained by means of a plumb-line. To 
see the spider’s lines in the field of the 
telescope at the same time with the 
star, a faint light should be placed 
near the object-glass. When the 
plumb-line, the star Alioth, and the 
north star, fall on the vertical spider’s 
line, the horizontal limb is firmly 
clamped, and the telescope brought 
down to the horizon ; a light, seen 
through a small aperture in a board, 
and held at some distance by an as¬ 
sistant, is then moved according to signals, until it is cov¬ 
ered by the intersection of the spider’s lines. A picket 
driven into the ground, under the light, serves to mark the 
meridian line for reference by day, when the angle formed 
by it and the magnetic meridian may be measured. 



6 


BOOK III. 


LEVELLING AND TOPOGRAPHICAL SURVEYING. 


SECTION I. 

( / 

OF LEVELLING. 

1« Levelling is the art of determining the relative dis¬ 
tances of points from the centre of the earth. 

2. A line whose points are all equally distant from the 
centre of the earth, is called a line of true level , and a sur¬ 
face, all whose points are equally distant from the centre 
of the earth, as the surface of still water, is called a level 
surface. 

3. One point is said to be above another, when it is 
farther from the centre of the earth; and this difference of 
distance from the centre, is called the difference of level be¬ 
tween the two points. 

4. A straight line drawn tangent to a line of true level 
at any point, is a horizontal line, and is called a line of 
apparent level. Thus (PI. 4, Fig. 1), if C is the centre of 
the earth and AEF a line of true level, ABB is a line of 
apparent level. This is the line of level determined by an 
instrument. The difference between the apparent and true 
level at any distant station B , as determined from A, is BE, 
or the excess of the secant of the arc AE over the radius. 

5. To find a general formula for computing this excess, 
we have (Greom. B. IV., Prop. XXX.) 

AB 3 = BE {BE + 2 EC ); 

but since the arc AE is very small in comparison with the 

10 




146 


ELEMENTS OF SURVEYING, [BOOK III 


radius of the earth, the arc AE will not differ sensibly from 
the tangent AB; the diameter 2EG may, for the same 
reason., be taken for the secant {BE + 2EG)\ hence, 

AE 2 — BE X2EG, or dividing by 2EG, 


BE= 


AE~ 

2EG 


( 1 ). 


If we take the mean diameter of the earth to be 7919 

AE 2 

miles, formula (1) gives BE= ygjg (2) : hence, 


The departure of the apparent from the true level , starting 
from a given point , is 'equal to the square of the distance to the 
second point , divided by the diameter of the earth. 


If in formula (2) you give to AE, in succession, every 
value from 1 chain to any given number of chains, (say 
100), and reduce at the same time both terms of the frac¬ 
tion to inches, a table may be computed as below. 

Table showing the differences in inches between the true and aq> 
parent level , for distances between 1 and 100 chains. 


Chains. 

Inches. 

Chains. 

Inches. 

Chains. 

Inches. 

Chains. 

Inches. 

1 

.001 

26 

.845 

51 

3.255 

76 

7.221 

2 

.005 

27 

.911 

52 

3.380 

77 

7.412 

3 

.011 

28 

.981 

53 

3.511 

78 

7.605 

4 

.020 

29 

1.051 

54 

3.645 

79 

7.802 

5 

.031 

30 

1.125 

55 

3.781 

80 

8.001 

6 

.045 

31 

1.201 

56 

3.925 

81 

8.202 

7 

.061 

32 

1.280 

57 

4.061 

82 

8.406 

8 

.080 

33 

1.360 

58 

4.205 

83 

8.612 

9 

.101 

34 

1.446 

59 

4.351 

84 

8.832 

10 

.125 

35 

1.531 

60 

4.500 

85 

9.042 

1 11 

.151 

36 

1.620 

61 

4.654 

86 

9.246 

; 12 

.180 

37 

1.711 

62 

4.805 

87 

9.462 

j 13 

.211 

38 

1.805 

63 

4.968 

88 

9.681 

I 14 

.245 

39 

1.901 

64 

5.120 

89 

9.902 

1 15 

.281 

40 

2.003 

65 

5.281 

90 

10.126 

16 

.320 

41 

2.101 

66 

5.443 

91 

10.351 

17 

.361 

42 

2.208 

67 

5.612 

92 

10.587 

18 

.405 

43 

2.311 

68 

5.787 

93 

10.812 

19 

.451 

44 

2.420 

69 

5.955 

94 

11.046 

20 

.500 

45 

2.531 

70 

6.125 

95 

11.233 

21 

.552 

46 

2.646 

71 

6.302 

96 

11.521 

22 

.605 

47 

2.761 

72 

6.480 

97 

11.763 

23 

.661 

48 

2.880 

73 

6.662 

98 

12.017 

24 

.720 

49 

3.004 

74 

6.846 

99 

12.246 

25 
— ■ 

.781 

50 

3.125 

7 5 

7.032 

100 

12.502 



































SEC. I] 


THE Y LEVEL. 


147 


Observing that for AE— 80 chains = 1 mile, BE is equal 
to 8.001 inches, or about two-thirds of a foot, arid since 
the differences of level vary as the squares of the dis 
tunces, we have the following easy rule for finding the cor 
reetion in feet. 

The correction for curvature , in feet , is equal to two-third* 
of the square of ike distance in miles . 

INSTRUMENTS. 

6. Before proceeding further in the discussion of the 
principles of levelling, we will describe some of the in¬ 
struments used, and first, 

THE Y LEVEL. 

7. A level is an instrument used to determine horizontal 
lines, and the difference of level of any two points on the 
surface of the earth. 

The part of the instrument shown in PI. 4, Fig. 2, rests 
on a tripod, to which it is permanently attached at Z. HEL 
is a horizontal brass plate, through which four levelling 
screws with milled heads are passed, and worked against a 
second horizontal plate GG. Two of these screws, K and 
f are seen in the figure. A is a clamp-screw, which, being 
loosened, allows the upper part of the instrument to turn 
freely around its axis. Q is a tangent-screw, by means of 
which the upper part of the instrument is moved gently, 
after the clamp-screw S has been made fast. EE is a hori¬ 
zontal bar, perpendicular to which are the wyes, designat¬ 
ed Y’s, that support the telescope LB. This telescope is 
confined in the Y’s by the loops r, r, which are fastened 
by the pins p and p. The object-glass B , is adjusted to 
its focus by the screw X j the eye-glass L slides out and 
in freely. The screws f f work the slide which carries 
the horizontal hair; and two horizontal screws, only one 
of which, a, is seen, work the slide that carries the verti¬ 
cal hair. CD is an attached spirit-level. The screw R 
elevates and depresses the Y, nearest the eye-glass. In 
some instruments this Y is elevated and depressed, by 
means of two screws at M and JtL 


143 


ELEMENTS OF SURVEYING. [BOOK III 


Before using this level, it must be adjusted. The ad¬ 
justment consists in bringing the different parts to their 
proper places. 

The line of collimation is the axis of the telescope. With 
this axis, the line drawn through the centre of the eye¬ 
glass and the intersection of the spiders lines, within the 
barrel of the telescope, ought to coincide. 

First adjustment.* To fix the intersection of the spidei J s 
lines in the axis of the telescope. 

Having screwed the tripod to the instrument, extend 
the legs, and place them firmly. Then loosen the clamp- 
screw Sj and direct the telescope to a small, well-defined, 
and distant object. Then slide the eye-glass till the spider’s 
lines are seen distinctly; after which, with the screw W, 
adjust the object-glass to its proper focus, when the object 
and the spider’s lines will be distinctly seen. Note now 
the precise point covered by the intersection of the spider’s 
lines. 

Having done this, revolve the telescope in the Y’s, half 
round, when the attached level CD will come to the upper 
side. See if, in this position, the horizontal hair appears 
above or below the point, and in either case, loosen the 
one, and tighten the other, of the two screws which work 
the horizontal hair, until it has been carried over half the 
space between its last position and the observed point. 
Carry the telescope back to its place; direct again, by the 
screws at M and i?, the intersection of the spider’s lines to 
the point, and repeat the operation, till the horizontal hair 
neither ascends nor descends while the telescope is revolv¬ 
ed. A similar process will arrange the vertical hair, and 
the line of collimation is then adjusted. 

Second adjustment. To make the axis of the attached 
level CD parallel to the line of collimation. 

Turn the levelling screws M and B, until the bubble 


* This, and same of the following adjustments, are so similar to those of the 
theodolite, that they would not be here repeated, but that some may use the 
level without wishing to study a more complicated instrument. 




SEC L] 


THE Y LEVEL. 


149 


of the level DC stands at the middle of the tube. Then 
open the loops, and reverse the telescope. If the bubble 
still stands at the middle of the tube, the axis of the level 
is horizontal; but if not, it is inclined, the bubble being 
at the elevated end. In such case, raise the depressed, or 
depress the elevated end, by means of the small screw h, 
half the inclination; and then with the screws, at M and R , 
bring the level to a horizontal position. Reverse the teles¬ 
cope in the Y’s, and make similar corrections again; and 
proceed, thus, until the bubble stands in the middle of 
the tube, in both positions of the telescope; the axis of the 
level is then horizontal. 

Let the telescope be now revolved in the Y’s. If the 
bubble continues in the middle of the tube, the axis of the 
level is not only horizontal, but also parallel to the line of 
eollimation. IfJ however, the bubble recedes from the centre, 
the axis of the level is inclined to the line of eollimation, 
and must be made parallel to it, by means of two small 
screws, which work horizontally; one of these screws is 
seen at q. By loosening one of them, and tightening the 
other, the level is soon brought parallel to the line of col- 
limation; and then, if the telescope be revolved in the Y’s, 
the bubble will continue at the middle of the point of the 
tube. It is, however, difficult to make the first part of this 
adjustment, while the axis of the level is considerably in¬ 
clined to the line of eollimation: for, allowing the level to 
be truly horizontal in one position of the telescope, after it 
is reversed, there will be but one corresponding position 
in which the bubble will stand at the middle of the tube. 
This suggests the necessity of making the first part of the 
adjustment with tolerable accuracy; then, having made the 
second with care, re-examine the first, and proceed thus 
till the adjustment is completed. 

Third adjustment. To make the level CD and the 
line of eollimation perpendicular to the axis of the instrument , 
or parallel to the horizontal bar EE. 

Loosen the clamp-screw /SJ and turn the bar EE, until 
level DC comes directly over two of the levelling 


150 


ELEMENTS OF SURVEYING. [BOOK III. 


screws. Bv means of these screws, make the level CD 
truly horizontal. Then, turn the level quite round; if, 
during the revolution, it continue horizontal, it must be at 
right angles to the axis of the instrument about which it 
has been revolved. But if, after the revolution, the level 
CD be not horizontal, rectify half the error with the screws 
at M and R, and half with the levelling screws. Then 
place the bar EE over the other two levelling screws, and 
make the same examinations and corrections as before; and 
proceed thus, until the level can be turned entirely around 
without displacing the bubble at the centre. When this 
can be done, it is obvious that the level DC and the line 
of collimation, are at right angles to the axis of the instru¬ 
ment about which they revolve; and since the axis is care¬ 
fully adjusted by the maker, at right angles to the bar EE 7 
it follows, that the line of collimation, the level DC, and 
the bar EE, are parallel to each other. 

The level is now adjusted. When used, however, it is 
best to re-examine it every day or two, as the work will 
be erroneous unless the instrument is accurately adjusted. 

THE WATER LEVEL. 

8. The Water Level is an instrument that possesses the 
advantage of never requiring adjustment , and also of being 
very cheap; in fact, any ordinary workman may con¬ 
struct one. Having no telescope, it is impossible to take 
long sights, but for such work as is required to be done 
by the ordinary surveyor, it gives very good results. 

Two brass cups, C and D, about one inch in diam¬ 
eter, and from four to five inches in height, are permanent¬ 
ly attached to a hollow brass tube of three feet long and 
half an inch in di- QE 
ameter. The cups 
are for the purpose A L_ 
of receiving the 
ends E and F of 
two bottles, the 
bottoms of which have been cut off. The bottoms may be 
cut off by means cf a hot iron, or file. The ends are fixed 
in their places with pucty. 



















SEC. 1] 


LEVELLING STAVES. 


151 


The projecting axis g works in a hollow cylinder h , 
which forma the top of a stand. The tube, when the level 
is required for use, is filled with water (colored with lake 
or indigo), till it nearly reaches the necks of the bottles. 
After placing the stand tolerably level by the eye, with¬ 
draw both corks, and the surface of the water in the bot-* 
ties will indicate a horizontal line in whatever direction the 
tube is turned. This level is well adapted to tracing con¬ 
tour lines as described in the next section. 


LEVELLING STAVES. 

9. The levelling staves are used to determine the points 
at which a given horizontal line intersects lines that are 
perpendicular to the surface of the earth, and to show the 
distances of such points of intersection from the ground. 

The levelling staff is a necessary accompaniment to 
either of the levels described. Several kinds are used. 

One of the best, consists of a staff 12 or 15 feet long, 
and graduated to feet, tenths, and hundredths. A sliding 
vane is made to move up or down by a 
cord and pulleys, and on the vane is a 
vernier, by means of which the reading 
of the staff may be effected to thou¬ 
sandths of a foot. AB represents a 
portion of the staff, DC the moveable 
vane , with an opening EF\ through which 
the graduation on the staff is seen. F is & 
the vernier of the vane, the 0 being de¬ 
termined by the transverse line DC. To 
render this line more distinct, the vane 
is divided into four quarters, and the 
alternate ones are painted black, which, 
by their contrast with the white quar¬ 
ters, show the line DC distinctly. 

10. Another variety of levelling staff is shown in PI. 4, 
Fig. 3. It is formed of two pieces, each about six feet 
long, 0113 of which slides in a groove of the other, and 
bears a vane similar to that already described. It is grad¬ 
uated to feet, bches, and eighths of an inch. The line of 



















152 


ELEMENTS OF SURVEYING. [BOOK III 


sight of the telescope is always directed to the centre of 
the vane. When the line of eight is less than six feet from 
the ground, the staff is reversed,—the vane run up the staff, 
and the readings made by means of the reversed figures at the 
right, where they are cut by the lower line of the vane. 
When the line of sight is more than six feet from the ground, 
the staff stands as in the figure, the reading is then made at 
the line be, and the figures indicating the height, are found on 
the sliding part which carries the vane. The reading of the 
staff, as it now stands, is seven feet. 

11. Another rod is sometimes used on which the figures 
are marked so plainly, that they may be read by the ob¬ 
server himself, without the aid of a vane; thus avoiding 
errors through ignorance or negligence of the rodman. 

If the telescope used, inverts the object, the figures should 
be made inverted on the staff, so as to appear erect. Each 
of the rods described, has its advantages, and either one ma) 
be used according to the circumstances of the survey. 

12. There is a method of testing the adjustments of the 
Y level, which ought not to be neglected, since all the re¬ 
sults depend on the accuracy of the instrument. The 
method is this: 

The level being adjusted, place it at any convenient 
point, as G (Fig. 4). At equal distances of about 100 yards, 
on either side, and in the same line with the level, place 
the levelling staves, CE\ BF. Make the level horizontal 
with the levelling screws. Then, turn it towards either 
staff, as BF, and run the vane up or down, as required, 
until the intersection of the hairs strikes the centre : then 
make the slide fast, and note carefully the height of the 
vane. Turn the level half round, and do the same in 
respect of the staff CE. 

Let the telescope be now reversed in the Y’s. Sight 
again to the staff BF, and note the exact height of the 
vane. Let the telescope be now turned half round, and 
the same be done for the staff CE. If the two heights 
last observed, are equal to those first noted, each to each, 
the line of collimation is perpendicular to the axis of the 


SEC. I.) 


OF LEVELLING 


153 


instrument, and if the bubble has, at the same time, pre- 
served its place at the middle point of the tube, the instru* 
ment is truly adjusted. 

For, had the line of collimation been inclined to the 
axis of the level, it would, in the first instance, have taken 
the direction AF or Ad; and when turned half round, it 
would have taken the direction AF or Ab. The telescope 
being reversed in the Y’s, and again directed to the staff 
BF\ the line of collimation would take the direction Ad or 
AF J and when turned to the staff CE : it would take the 
direction Ab or AF : and the two distances BF\ Bd 1 or Cb. 
CE\ can only be equal to each other when the line of col 
4 limation falls on the horizontal line gf 


LEVELLING IN THE FIELD. 

13. The operation of levelling may be undertaken: 

1st. For the purpose of determining the difference oi 
level between two given points. 

2d. For the purpose of obtaining a section or profile 
along a given line, as in the reconnoissance for a line of 
railroad. 

3d. For the purpose of determining the contour lines in 
a topographical survey, as described in the next section. 


DIFFERENCE OF LEVEL BETWEEN TWO POINTS. 


14. When it is proposed to find the difference of level 
of any two objects, or stations, all levels made in the di¬ 
rection of the station at which the work is begun, are 
called, for the sake of distinction merely, bach-sights; and 
levels taken in the direction of the other station, /ore- 
sights. 


Before going on the field with the leve‘ rule three 
columns, as below, and head them, stations, back-sights, 
fore-sights. 


154 


ELEMENTS OF SURVEYING. [BOOK III 


FIELD NOTES. 


Stations. 

Back-Sights. 

— Fore-Sights. 

1 

10 

3 

2 

11-6 

0 

3 

6-8 

4-9 

4 

3-9 

8-3 

Sums . . 

Dif. of level. 

. . . 31-11 

16-00 

. . . 15-11 

16-0 


EXAMPLE. 

Find the difference of level between any two points , as A and 

G (PI. 4, Fig. 5.) 

The level being adjusted, place it at any point, as B , as 
nearly in the line joining A and G as may be convenient. 
Place a levelling staff at A, and another at JV, a point 
lying as near as may be in the direction of G. Make the 
level horizontal, by means of the levelling screws; turn the 
telescope to the staff at A, and direct the person at the 
staff to slide up the vane until the horizontal line ah pierces 
its centre; then note the distance Ah (equal to 10 feet in 
the present example), and enter it in the column of back¬ 
sights, opposite station 1. Sight also to the staff at iVJ and 
enter the distance JSfa, equal to 3 feet, in the column of fore¬ 
sights, opposite station 1. 

Take up the level, and place it at some other convenient 
station, as C\ and remove the staff at A , to M. Having 
levelled the instrument, sight to the staff at N, and enter 
the distance Nd, 11 feet 6 inches, in the column of back¬ 
sights, opposite station 2 : sight also to the staff at M ) and 
enter the distance Mf equal 0, in the column of for e-sights, 
opposite station 2. 












SEC. I.J 


OF LEVELLING. 


155 


Let the level be now removed to any other station, as 
D, and the staff at E, to some other point, as P. Let the 
distance Mg, equal to 6 feet 8 inches, be entered in the 
column of back-sights, opposite station 3, and the distance 
Ph, equal to 4 feet 9 inches, in the column of fore-sights. 
Let the instrument bo now placed at E , and the distance 
Pm, equal to 3 feet 9 inches, and Gn, equal to 8 feet 3 
inches, be entered opposite station 4, in their proper 
columns. 

It is evident from the figure, that the difference of level 
NF, between A and E, is equal to the back-sight bA, dim¬ 
inished by the fore-sight aE; also that the difference of 
level between E and M is equal to the back-sight dE, dim¬ 
inished by the foresight 0, and since each set of obser¬ 
vations is entirely independent of every other set, we may 
infer that the difference of level between two points as determin¬ 
ed by one position of the level, is equal to the bach-siglit, dim¬ 
inished by the fore-sight. If the fore-sight be greater than the 
back-sight, the difference will be affected with a minus sign, 
a result which shows that the second point is lower than 
the first. Generally, the difference of level between any two 
points, determined as above, is equal to the sum of the back¬ 
sights diminished by the sum of the fore-sights. If the result is 
plus, the second point is higher than the first; if negative, 
it is lower. 

In the example given, the difference of level between 
A and G, is 15 feet 11 inches. 

15. In the previous example, we did not regard the dif¬ 
ference between the true and apparent level. If it be ne¬ 
cessary to ascertain the result with extreme accuracy, this 
difference must be considered: and then, the horizontal 
distances between the level, at each of its positions, and the 
staves, must be measured, and the apparent levels dimin¬ 
ished by the differences of level; which differences can be 
found from the table. 


156 


ELEMENTS OF SURVEYING. [B.OOK III 


THE FOLLOWING IS SUCH AN EXAMPLE. 


Stat. 

Back-sts. 

Distances. 

Fore-st. 

Distances. 

i --■■■ 

Cor.back-sights 

Ccr. fore-st*. 

1 

9-8 

20 eh. 

1-6 

32 ch. 

9-7.500 

1-4.720 

2 

8-7 

25 ch. 

2-4 

28 ch. 

8-6.219 

2-3.019 

3 

5-2 

18 ch. 

3-1 

16 ch. 

5-1.595 

3-0.680 

4 

10-3 

29 ch. 

1-9 

87 ch. 

10-1.949 

0-11.538 

5 

11-0 

45 ch. 

2-5 

72 ch. 

10-9.469 

1-10.520 


44-2.732 

9-6.477 


In this example, the first column shows the stations; 
the second, the back-sights; the third, the distances from 
the level in each of its positions to the back staff; the 
fourth, the fore-sights; the fifth, the distances from the 
level to the forward staff; the sixth and seventh, are the 
columns of back and fore-sights, corrected by the difference 
of level. The corrections are thus made:—The difference 
of level in the table corresponding to 20 chains, is 5 tenths 
of an inch, which being subtracted from 9 feet 8 inches, 
leaves 9 feet 7.5 inches for the corrected back-sights; this 
is entered opposite station 1 in the sixth column. The dif¬ 
ference of level corresponding to 32 chains, is 1.280 inches, 
which being subtracted from the apparent level, 1 foot 6 
inches, leaves 1 foot 4.720 inches for the true fore-sight 
from station 1. The other corrections are made in the 
same manner. 

The sum of the back-sights being 44 feet 2.732 inches, 
and the sum of the fore-sights 9 feet 6.477 inches, it fol¬ 
lows, that the difference, 34 feet 8.255 inches, is the true 
difference of level. 

16. In finding the true from the apparent level, we 
have not regarded the effect caused by refraction on the 
apparent elevation of objects, as well because the refraction 
is different in different states of the atmosphere, as because 
the corrections are inconsiderable in themselves. 

17. The small errors that would arise from regarding 
the apparent as the true level, may be avoided by placing 

























SEC. I.] 


OF LEVELLING. 


157 


the levelling staves at equal distances from the level. In such 
case, it is plain, 1st, that equal corrections must be made 
in the fore and back-sights; and, 2dly, that when the fore 
and back-sights are diminished equally, the result, which is 
always the difference of their sums, will not be affected. 

This method should always be followed, if practicable, 
as it avoids the trouble of making corrections for the dif¬ 
ference of true and apparent level. 

The differences between the true and apparent level, 
being very inconsiderable for short distances, if only ordi¬ 
nary accuracy be required, it will be unnecessary to make 
measurements at all. Care, however, ought to be taken, 
in placing the levelling staves, to have them at as nearly 
equal distances from the level as can be determined by the 
eye; and if the distances are unequal, let the next distances 
also be made unequal; that is, if the back-sight is the 
longer in the first case, let it be made proportionably 
shorter in the second, and the reverse. 

LEVELLING FOR SECTION. 

18. Having decided upon the line along which a section 
is to be taken, let a permanent mark be made at the be¬ 
ginning of the line: this is called a bench-marJc. A bench¬ 
mark is made by drilling a hole in a rock, or by painting 
upon a rock or fence, or sometimes by driving a stake in 
the ground, with its upper end marked by a nail-head. 
Bench-marks should be made from time to time along the 
line, to serve as checks, in case a re-survey should become 
necessary. 

The operations in the field are similar to those in the 
last example, and the field notes are kept in the same 
manner, except that a new column is added for bearings, 
when it is necessary to make a plot of the line of survey. 
The total distance of each point above or below the start¬ 
ing point may be computed, and written in a separate col¬ 
umn, paying particular attention to the signs. We annex 
an example, in which the heights are estimated in feet, 
and decimals of a foot. 


158 


ELEMENTS OF SURVEYING. [BOOK III 


Sta¬ 

tion. 

Distances in 

feet. 

B. Sight. 

F. Sight. 

Dif. between 

B. S. and F. S. 

Total Dif. of 
Level. 

-- 

REMARKS. 

1 

650 

2.35 

14,55 

-12.20 

— 

12.20 

Commenced at bench-mark A. 

2 

700 

3.56 

9.58 

- 6.02 

— 

18.22 


3 

750 

10.34 

6.21 

+ 4.13 

— 

14.09 


4 

650 

14.55 

0.25 

+14.30 

+ 

0.21 


5 

600 

9.98 

1.67 

+ 8.31 

+ 

8.52 


6 

650 

3.62 

14.54 

-10.92 

— 

2.40 



B.M 

1.23 

13.45 

-12.22 

— 

14.62 

Bench mark on rock. 

7 

500 

2.23 

12.05 

- 9.82 

— 

24.44 

Terminating at BM on oak tree. 

8 

750 

6.20 

19.55 

- 13.35 

— 

37.79 



The fifth column shows the difference of level between 
any two consecutive positions of the levelling staff, and ia 
found by subtracting the fore-sight from the corresponding 
back-sight, and giving to the remainder the proper sign. 
The sixth column shows the distance of each point above 
or below the bench-mark A, and is obtained by continual 
additions of the numbers in column 5. Thus, 

(- 12.20) + (- 6.02) = - 18.22 ; (- 18.22) + 4.13 = - 14.09; 
and so on. 

It will be seen that the point of termination is 37.79 
feet below the starting point. 

PLOTTING THE SECTION OR PROFILE. 

19. The vertical distances being generally very small as 
compared with the horizontal distances, two different scales 
become necessary in plotting a profile. In order that the 
vertical distances may be fully exhibited in the plan, the 
scale used for them is much larger than is used for lines 
measured in a horizontal direction. This becomes absolutely 
necessary where long lines of profile, with a gentle slope, 
are to be plotted, as is always the case in the trial section 
of a railroad survey. We shall illustrate the manner of 
plotting, by drawing the section determined by the field* 
notes just given. 

20. Draw a horizontal line AK. called a datum line, and 

7 i 



























SEC. II] TOPOGRAPHICAL SURVEYING. 


159 


assume some point as A, to represent the point of begin¬ 
ning: lay off on the datum line, distances equal to the 


L 



measured distances 650, 700, 750, &c., feet to If, using in 
this case a scale of 1500 feet to 1 inch. At the points B, 
C, D, E, &c., thus determined, erect perpendiculars, making 
them equal, on a scale of 25 feet to the inch, to the cor¬ 
responding differences of level taken from the field-book; 
through the points thus found, draw the irregular line 
APLM, and it will represent the surface of the ground 
along the line of level. 

The bench-mark, between stations 7 and 8, is not plotted, 
as it is supposed to be out of the line of the section, and 
no distances are measured to it. 


SECTION II. 

TOPOGRAPHICAL SURVEYING. 

21. Besides the surveys that are made to determine the 
area of land and the relative positions of objects, it is fre¬ 
quently necessary to make minute and careful examinations 
for the purpose of ascertaining the form and accidents of 
the ground, and to make such a plan as will distinguish 
the swelling hill from the sunken valley, and the course 
of the rivulet from the unbroken plain. 










160 


ELEMENTS OF SURVEYING. [BOOK III 


22. This branch of surveying is called Topography. In 
surveys made with a view to the location of extensive 
works, the determination of the slopes and irregularities of 
the ground is of the first importance: indeed, the examina¬ 
tions would otherwise be useless. 

23. The manner of ascertaining these irregularities is, to 
suppose the surface of the ground to be intersected by a 
system of horizontal planes at equal distances from each 
other; the curves determined by these secant planes, being 
lines of the surface, will indicate its form at the places of 
section, and, as the planes are nearer or more distant from 
each other, the form of the surface is more or less accu¬ 
rately ascertained. 

If such a system of curves be determined, and then pro¬ 
jected or let fall on a horizontal plane, it is obvious that 
the curves on such plane will be nearer together or farther 
apart, as the ascent of the hill is steep or gentle. 

If, therefore, such intersections be made, and the curves 
so determined be accurately delineated on paper, the map 
will give such a representation of the ground as will 
show its form, its inequalities, and its striking character¬ 
istics. 

24. The subject divides itself, naturally, into two parts. 

1st. To make the necessary examinations and measure¬ 
ments on the field; and, 

2d. To make the delineations on paper. 

For the former of these objects, the theodolite is the 
best instrument; the common level, however, will answer 
all the purposes, though it is less convenient. 

Before going on the field, it is necessary to provide a 
number of wooden stakes, about two feet in length, with 
heads. These stakes are used to designate particular points, 
and are to be driven to the surface of the ground. A 
nail should then be driven into the head of each of them, 
to mark its centre. 

25. We shall, perhaps, be best understood, by giving an 
example or two, and then adding such general remarks as 


SEC. II.] TOPOGRAPHICAL SURVEYING. 


101 


will extend the particular cases to all others that can 

occur. 

Let A (PI. 4, Fig. 6), he the summit of a hill, the con¬ 
tour of which it is required to represent. At A, let a 
stake be driven, and let the axis of the theodolite, or level, 
be placed directly over the nail which marks its centre. 
From A, measure any line down the hill, as AB , using the 
telescope of the theodolite or level to arrange all its points 
in the same vertical plane. Great care must be taken to 
keep the measuring chain horizontal, for it is the horizontal 
distances that are required. At different points of this line, 
as a, h, c, d, &c. ; let stakes be driven, and let the horizon 
tal distances Aa, ah, he , and cd, be carefully measured. In 
placing the stakes, reference must be had to the abruptness 
of the declivity, and the accuracy with which the surface 
is to be delineated: their differences of level ought not to 
exceed once and a half, or twice, the distance between the 
horizontal planes of section. 

Having placed stakes, and measured all the distances 
along the line AB, run another line down the hill, as AC\ 
placing stakes at the points e, f g , and h, and measuring 
the horizontal distances Ae, ef, fg , and gh. Eun also the 
line AD , placing stakes at i, l, m, and n , and measuring 
the horizontal distances Ai, il, Im , and mn. 

Each line, AB, AC, AD, running down the hill from A, 
may be regarded as the intersection of the hill by a verti¬ 
cal plane; and these secant planes are to be continued over 
all the ground which is to be surveyed. If the work is 
done with a theodolite, or with a level having a compass, 
the angles DAB and BAC, contained by the vertical se¬ 
cant planes, can be measured; if it is done with a level, 
having no needle, let any of the distances ae, hf, ai, hi, &c., 
be measured with the chain, and there will then be known 
the three sides of the triangles Aae , Ahf Aai, Abl, &c. 

Let now, the difference of level of the several points 
marked in each of the lines AB, AD, AC, be determined. 

In the present example the results of the measurements 
and levelling, are— 


11 


162 


ELEMENTS OF SURVEYING. [BOOK ID 


Line AB. 

Difference of Level. 

A above a 12 feet 
a above b 8 “ 

b above e 9 “ 
c above d 11 “ 

Line AC. 

Difference of Level. 

A above e 11 feet 
e above / 9 “ 

/ above g 12 “ 

g above h 14 “ 

Line AD. 

Difference of Level. 

A above i 9 feet 
i above Z 13 11 

l above m 7 “ 

m above n 14 “ 

Angle CAB = 25°, Angle DAB = 30°. 

These data are sufficient, not only to find the interseo 
tions of horizontal planes with the surface of the hill, but 
also for delineating such curves of section on paper. 

Having drawn on the paper the line AB , lay off the 
angle BA C = 25°, and the angle BAD = 30°. Then, from 
a convenient scale of equal parts, lay off the distances Aa. 
ab, be , cd, Ae , ef, fg , g\ Ai, il, Im , and mn. 

Let it be required that the horizontal planes be at a 
distance of eight feet from each other. Since A is the 
highest point of the hill, and the difference of level of the 
points A and a, is 12 feet, the first plane, reckoning down 
wards, will intersect the line traced on the ground from A 
to B , between A and a. Regarding the descent as uniform, 
which we may do for small distances without sensible error, 
we have this proportion; as the difference of level of the 
points A and a, is to the horizontal distance Aa, so is 8 
feet, to the horizontal distance from A to where the first 


Distances. 

Aa = 40 feet 
ab = 50 “ 

be = 30 “ 
cd = 46 “ 


Distances. 

At — 28 feet 
ef = 45 “ 

fg = 55 “ 

gh = 49 “ 


Distances. 
Ai =25 feet 
il — 55 11 
Im =38 “ 
mn = 48 “ 





SEC. 11.] TOPOGRAPHICAL SURVEYING. 


163 


horizontal plane will cut the line from A to B. This dis¬ 
tance being thus found, and laid off from A to o, gives o, 
a point of the curve in which the first plane intersects the 
ground. The points at which it cuts the line from A to (7, 
and the line from A to D, are determined similarly, and 
three points in the first curve are thus found. 

The graphic operations are greatly facilitated by the aid 
of the sector. Let it be borne in mind, that the descent 
from A to a, is 12 feet, and that it is required, upon the 
supposition of the descent being uniform, to find that part 
of the distance corresponding to a descent of 8 feet. Take 
the distance from A to a, in the dividers, and open the 
arms of the sector until the dividers will reach from 12 on 
the line of equal parts, on one side, to 12 on the line of 
equal parts, on the other. Then, without changing the 
angle, extend the dividers from 8 on one side, to 8 on the 
other; this will give the proportional distance to be laid 
off from A to o. Or, if the dividers be extended from 4 
to 4, the proportional distance may be laid off from a 
to o. 

If the distances to be taken from the sector fall too 
near the joint, let multiples of them be used ; as for in 
stance, on the French sectors, let the arms be extended 
until the dividers reach from 120 on the one, to 120 on 
the other, then 80 or 40 will be the proportional numbers. 
Other multiples may be used, though it is generally more 
convenient to multiply by 10. 

26. The second plane is to pass 8 feet below the first, 
that is, 16 feet below i, or 4 feet below a, a being 12 feet 
below A. Take the distance ab in the dividers, and ex¬ 
tend the sector, so that the dividers will reach from 8 to 
(the descent from a to b being 8 feet) 8, or from 80 to 
80; then, the distance from 4 to 4, or from 40 to 40, being 
laid off from a to jp, gives p, a point of the second curve. 

The difference of level between a and b being 8 feet, 
and the difference of level between a and p being 4 feet, 
the difference of level between p and b must also be 4 
feet; hence, the third plane will pass 4 feet below b : and 


164 


ELEMENTS OF SURVEYING. [BOOK III 


q, determined as above, is a point of the third curve, and 
so on. After having determined the points in which each 
contour line cuts the lines diverging from A, let the con¬ 
tour lines be drawn through them, so as to indicate the 
surface of the hill. The numbers (8), (16), &c., show the 
vertical distances of the respective planes below the point A. 

27. Having drawn the horizontal curves, the next thing 
to be done is so to shade the drawing that it may represent 
accurately the surface of the ground. This is done by 
drawing a system of small broken lines, as in the figure, 
perpendicular in direction to the horizontal curves already 
described. In all topographical representations of undulat¬ 
ing ground, the lines of shading are drawn perpendicular to 
the horizontal curves. 

A profile along either of the diverging lines may be 
plotted by the rules already given (Art. 20.) The diagram 
shows the profile along the line AB. 


a 



28. The following example will illustrate the methods 
employed in making a topographical survey, where great 
accuracy is required. 


By means of a theodolite or level, range a line of stakes 
A } By Cy Dy Ey &c., along one side, or through the middle of 
the ground to be surveyed, at equal and convenient distances 
from each other, say 50 feet apart. Mark, with a piece of 
red chalk, on each stake in this row, one of the letters of 
the alphabet, A, B, Cy D , Ey &c., in their order. At A, 
range a line of stakes, perpendicular to AE, planting the 
stakes at intervals of 50 feet; and mark them with the 

letters A A &c, which are read A first, A second, 
A third, &c. 





SEC. II.] TOPOGRAPHICAL SURVEYING. 


165 


B 

A 

l 

A 

z 

A 

2 

A 

4 


3 

B 

B 

73 

3 


t 

z 

3 

4 

£ 

C 



b 



C 

C 

a 

c 

C 

D 

1 

t 

3 

4 

* 

B 

D 

D 

D 

1) 


1 

z 

a 

4 

s 




a 



E 

El 

Ez 

E3 

E4 

Es 


At B , range a line of stakes also perpendicular to AE, 
and at distances of 50 feet from each other, and designate 

them -A ^ &c. Do the same at (7, D, E, &c., until all 

the stakes are placed, dividing the area to be surveyed 
into squares of 50 feet on a side. The letters and figures 
should be plainly marked on a smooth face of each stake, 
for facility of reference. If this system of notation be fol¬ 
lowed, the stakes may be recorded without danger of con¬ 
fusion. 

The next operation is to determine the difference of 
level between each stake, and some fixed horizontal plane, 
which is called a plane of reference. If the sea is near, the 
plane of mean low water, may be taken as the plane of 
reference. If not, assume the horizontal plane, passing 
through the lowest point of the ground to be surveyed, and 
make a permanent bench-mark at the point of beginning. 
If the lowest point cannot be easily determined, assume 
such a plane of reference as shall pass quite below the low¬ 
est point of the ground. 

In the example, which we have taken for illustration, 
the stake ^ is at the lowest point, and let us assume the 
plane of reference to pass through that point. 














160 


ELEMENTS OF SURVEYING. [BOOK IIL 


Set up the level at some convenient point, as a , take the 

reading of a levelling staff, set up at ^ and enter this 

reading as a back-sight. Then take the readings of the 
staff, at as many stakes as can be reached from the posi¬ 
tion a of the level, entering them as fore-sights. Endeavor¬ 
ing to make the last reading as small as possible. At this 

last stake Q drive a small peg for a bench-mark. 

Move the level to a second point &, and take a back¬ 
sight to the bench-mark (6T), and fore-sights, to as many 
stakes as possible. The following is the form of a field- 
book, used in topographical levelling. 

FIELD NOTES. 




Back-sights. 

Fore-Sights. 

Difference 

Total dif.of level 

above E 3 

Remarks, 

Object 

Reading 

Object 

Reading 



Object 

Reading 








E3 

0.000 


E3 

11.432 

D3 

1.211 

+ 10.221 

D3 

10.221 




C4 

0.897 

+ 

0.314 

C4 

10.535 

Check 10.585 

C4 

11.112 

E2 

5.281 

+ 

5.831 

E2 

16.366 




E4 

6.154 

— 

0.873 

E4 

15.493 




D4 

6.001 

+ 

0.153 

D4 

15.646 




D2 

1.182 

+ 

4.819 

D2 

20.465 




C3 

2.917 

— 

1.735 

C3 

13.730 




B5 

6.080 

— 

3.163 

Bo 

15.567 




C5 

0.921 

+ 

5.159 

C5 

20.726 




B4 

0.113 

+ 

0.808 

B4 

21.534 

Check 10.999 

B4 

11.882 

El 

8.019 

+ 

3.863 

El 

25.397 

21.534 



B3 

3.990 

+ 

4.029 

B3 

29.426 




Dl 

4.118 

— 

0.128 

Dl 

29.298 




C2 

1.880 

+ 

2.233 

C2 

31.536 




A4 

5.000 

— 

3.120 

A4 

28.416 




A5 

9.928 

— 

4.928 

A 5 

23.488 




D5 

1.675 


8.253 

D5 

31.741 




E5 

1.111 

+ 

0.564 

E5 

32.305 




A3 

0.108 

+ 

1.003 

A3 

33.308 




Cl 

0.004 

+ 

0.104 

Cl 

33.412 

Check 11.878 

Cl 

11.149 

B2 

4.181 

+ 

6.968 

B2 

40.380 

33.412 



Bl 

2.0G8 

+ 

2.173 

Bl 

42.553 




A2 

0.817 

+ 

1.191 

A2 

43.744 

Check 10.332 









43.744 

A2 

10.102 

A1 

4.332 

+ 

5.770 

Al 

49.514 

Check 5.770 









49.514 



































fi£C. II.] TOPOGRi PHICAL SURVEYING 


167 


If we subtract the first fore-sight (D3), from the back¬ 
sight (E3), the difference, entered in the column headed 
difference, is evidently the height of (D3), above the plane 
of reference through (E3); and we accordingly enter it 
under the column headed total diff. of level, as well as in 
the column of differences. If we subtract the fore-sight 
(C4) from the fore-sight (D3), the difference, entered in the 
column of difference, is evidently the height of (C4) above 
(7)3); if we now add this difference to the previous total, 
we shall find the height of (C4) above (E3). Subtracting 
the fore-sight (E2) from the back-sight (C4), we get the dif¬ 
ference of level between (E2) and (C4) which, added to the 
previous total, gives the height of (E2), above the stake 
(E3). In subtracting the fore-sight (E4) from the fore-sight 
(E2), we find a negative result which shows that (E4) is 
below (E2). We enter, then, this difference with its neg¬ 
ative sign, and to get the total, we subtract this difference 
from the previous total, and so on. 

As a check on the accuracy of our computation, sub¬ 
tract the fore-sight (04) from the back-sight (E3), and the 
difference will give the height of (C4), above the plane of 
reference. 

Again, subtract the fore-sight (B4) from the back-sight 
(C4), and add the remainder to the height of (C4,) and we 
shall find the height of (B4), which should agree with the 
height found under the heading, total diff. of level; and so 
oti for each time the level is moved. 

PLOTTING THE WORK. 

29. Draw, on a piece of paper, a straight line AK 
From a scale of equal parts, set off distances AB, BC, 
&c., each to represent 50 feet. Erect perpendiculars at 
each of the points A, B, G, &c., and then set off the distan¬ 
ces from A to 2, from 2 to 3, &c., each to represent 50 
feet; and through the points 2, 3, 4 and 5, draw parallels 
to AE. These, by their intersections with the lines drawn 
through A, B, C , &c., will determine the position of the 

stakes, ^ &c .; and write in red ink on the plot, the 


168 


ELEMENTS OF SURVEYING. [BOOK IIL 


height above the plane of reference of each stake, taken from 
the column of total differences in the field-book. Let us sup¬ 
pose that the horizontal planes are to be taken at distances 
of 6 feet We may find the points in which the contour 



lines intersect the lines at right angles, by the previous 
method, or perhaps still better, let the Surveyor take the 
plot thus commenced into the field, and by the eye trace 
the contour lines on the map. If we note where the lines 
at right angles cut fences, roads, streams, &c., we can, by 
joining the points, obtain a plot of the ground. 

30. The contour lines may be found as follows: Set up 
the level at a, and observe that the back-sight, to the stake, 
placed at (i?3), gave a reading of 11.432. Depress the 
vane equal to the distance between the horizontal secant 
planes, that is, 6 feet, which is done by placing it at the 
reading 5.432. Then direct the rodman, by signals up or 
down the hill, till the horizontal hair of the telescope coin¬ 
cides with the horizontal line of the vane. The foot of the 
staff is then 6 feet above the first point. Let a stake, 
marked 6, be driven here, and direct the rodman around 
the hill, until a second position shall be found, when the 


















SEC. II] TOPOGRAPHICAL SURVEYING. 


169 


horizontal hair of the telescope will cut the vane, and drive 
there another stake, marked 6; and so on, until a sufficient 
number of stakes have been driven to determine the curve 
(#)• Then, let the line of stakes, marked 6, be surveyed 
with the compass and chain, and plotted. Other contour 
lines may be found in a similar manner. 

31. We will add another example for determining the 
contour of an undulating piece of ground (PI. 4, Fig. 
7,) by means of horizontal sections. Let rows of stakes 
DA, HE\ IF\ &c., be driven at intervals, depending upon 
the required accuracy of the survey, and let f g , li , &c., 
be stakes driven along the lines, at such points as will 
best show the accidents of ground. Determine as before 
the difference of level between each stake, and some fixed 
point, and then determine where the contour lines cut the 
lines AD, EH, &c., by the rules already laid down. 

After the stakes are all placed, and the distances meas 
ured, let the differences of level of all the points so desig 
nated be found. In the present example, the results of the 
measurements are, 


Ft. 

Aa = 80 

AE— 

Ft. 

100 

EF— 100 

FG = 100 

ab = 60 

Ef = 

105 

Fi = 74 

Gm= 96 

= 90 

fy = 

85 

Ik =115 

mn = 76 

cd = 55 

gli = 

71 

hi = 60 

np = 76 

dD =50 

hH = 

74 

II = 86 

pL = 87 


Of the Levelling. 


Line AD. 

Line EH 

Line FI 

Line GL. 

Ft. 

Ft. 

Ft. 

Ft. 

A above d 5 

A below A 3 

F below E 2 

G below' F 1 

a 11 b 6 

Fj above J 9 

F above % 3 

G above 771 2 

b “ c 7 

f “ 9 3 

i “ k 5 

m 11 n 1 

C below d 2 

9 “ *1 

k “ 1 2 

n u p 2 

d above D 4 

Jl below II 3 

l below I 3 

p : eK)W I 4 


GB — 100 
Bq = 76 

qs = 85 

st = 127 
tO = 47 


Line BC 

TV 

B below G 2 

B above q 3 

q 11 s 2 
5 “ *3 

t below c 5 


The heights of the points are here compared with each 
other, two and two. Before, however, we can conceive 










170 


ELEMENTS OF SUP YEYING. [BOOK TIL 


clearly tlieir relative heights, we must assume some one 
point, and compare all tire others with it. Let the point 
A be taken. The height of 





Ft. 




Ft. 




Ft. 




Ft. 

A above 

a 

5 

A above/ 

12 

A above h 

13 

A above p 

11 

A 

it 

b 

11 

A 

it 

9 

15 

A 

u 

l 

15 

A 

u 

L 

7 

A 

it 

c 

18 

A 

it 

h 

16 

A 

tt 

I 

12 

A 

u 

B 

8 

A 

It 

d 

16 

A 

it 

H 13 

A 

it 

G 

6 

A 

u 

9 

11 

A 

a 

D 

20 

A 

it 

F 

5 

A 

tt 

m 

8 

A 

u 

s 

13 

A 

a 

F 

3 

A 

it 

i 

8 

A 

it 

n 

9 

A 

a 

t 

16 


And of A above C : 11 feet. 


This being done, a mere inspection shows us the high¬ 
est and lowest points, as also the relative heights of the 
others, reckoning upwards or downwards. Let them be 
now written in the order of their heights above the lowest 
point, which is B. The difference of level between A and 
B being 20 feet, if the difference of level of each of the 
points below A, be taken from 20 feet, the remainder will 
be the height above B. Arranging them in their order, 
we have 





Ft 




Ft. 




Ft. 




Ft. 

c 

above D 

2 

H above D 

7 

p above D 

9 

B above D 

12 

d 

it 

D 

4 

k 

a 

D 

7 

9 

tt 

D 

9 

L 

u 

B 

13 

h 

u 

D 

4 

s 

it 

D 

7 

O 

tt 

D 

9 

G 

a 

D 

14 

t 

n 

D 

4 

f 

a 

D 

8 

n 

tt 

D 

11 

a 

tt 

B 

15 

9 

u 

D 

5 

I 

it 

D 

8 

• 

i 

it 

D 

12 

F 

it 

B 

15 

l 

tt 

D 

5 

b 

tt 

D 

9 

m 

a 

D 

12 

E 

a 

B 

17 


A above B , 20 feet. 


In this example, the plane of reference is assumed 
through D, the lowest point of the ground; and the secant 
planes are taken 3 feet apart. 

32. The manner of shading the map, so as to indicate 
the hills and slopes, consists in drawing the lines of shad¬ 
ing perpendicular to the horizontal curves, as already ex 
plained. These shading lines are drawn close together, 
when the slope is abrupt, and further apart, as it grows 
more gentle. Fig. 7 indicates the method of shading. 








SEC, TL] TOPOGRAPHICAL SURVEYING. 


171 


33. When the plane of reference is so chosen that the 
points of the work fall on different sides of it, all the re¬ 
ferences on one side are called positive, and those on the 
other, negative. The curves having a negative reference 
are distinguished by placing the minus sign before the 
number ; thus — ( ). 

34. In topographical surveys, great care should be taken 
to leave some 'permanent marks , with their levels written 
on them in a durable manner. For example, if there are 
any rocks, let one or more of them be smoothed, and the 
vertical distance from the plane of reference marked there¬ 
on: or let the vertical distance of a point on some promi¬ 
nent building, be ascertained and marked permanently on 
the building. Such points should also be noted on the 
map, so that a person, although unacquainted with the 
ground, could by means of the map, go upon it, and trace 
out all the points, together with their differences of level. 

35. Besides representing the contour of the ground, it 
is often necessary to make a map which shall indicate the 
cultivated field, the woodland, the marsh, and the winding 
river. For this, certain characters, or conventional signs, 
have been agreed upon, as the representatives of things, 
and when these are once fixed in the mind, they readily 
suggest the objects for which they stand. Those which 
are given in Plates 5 and 6, have been adopted by the 
Engineer Department, and are used in all plans and maps 
made by the United States Engineers. 

It is very desirable that a uniform method of deline¬ 
ation should be adopted, and none would seem to be of 
higher authority than that established by the Topographi¬ 
cal Bureau. It is, therefore, recommended, that the con¬ 
ventional signs given in Plates 5 and 6, be carefully 
studied and uniformly followed. 


I 




BOOK I y. 

GEODESIC, TRIGONOMETRIC AND MARITIME 

SURVEYING 


SECTION I. 

I 

GEODESIC AND TRIGONOMETRIC SURVEYING. 

1. When a large extent of territory, or a long line of 
sea-coast is to be surveyed, it becomes necessary to con¬ 
sider the curvature of the earth’s surface; this branch of 
surveying is called Geodesic surveying. 

2. Extensive geodesic operations prove that the earth 
is an oblate spheroid, the shortest diameter of which coin¬ 
cides with the terrestrial axis, and all of whose meridians, 
are equal ellipses. The meridian lines, however, differ so 
little from the circumferences of circles, that they may be 
taken for them, except when great accuracy is required. 
The earth, will, therefore, in the following pages, be re¬ 
garded as a perfect sphere. 

3. The operations necessary to the successful execution 
of a Geodesic Survey, require the minutest attention, and 
when performed, numerous corrections are to be applied to 
the measured lines and angles, on account of the various 
causes of error incident to such operations. 

To investigate those causes of error, and to deduce rules 
for correcting the errors, in all cases, would far exceed 
the limits of an elementary treatise. We shall, therefore, 
attempt nothing more than a brief outline of the operations 



SEC. I.] 


TRIANGULATION. 


173 


of a trigonometric survey, with the application of some of 
the more important corrections. 

4. It may be observed that most of the operations de¬ 
scribed in this section, are equally applicable, whether we 
regard the area surveyed as plane or spherical: in either 
case, the basis of an accurate survey, is an extensive sys¬ 
tem of triangulation. 

5. After having made a preliminary examination or re¬ 
connaissance of the territory to be surveyed, suitable stations 
are selected at the most prominent points, and these points 
are marked by staves or signals. 

A base line is then measured. The length of the base 
will, in general, depend upon the magnitude of the survey, 
and each extremity is marked by a signal. 

The next step is the triangulation. At each extremity 
of the base, the angles between the base, and the lines 
drawn to each of the visible signals, are carefully meas¬ 
ured by means of a theodolite. The sides of the triangles 
thus obtained, serve as new bases upon which other trian¬ 
gles may be formed, and so on, until the entire area is 
covered by a net-work of triangles. 

6. This system of triangles is called the 'primary system, 
and the operation of forming them is called the primary 
triangulation. Within the primary triangles, and depending 
upon them, a system of smaller triangles is formed in the 
same manner, called the secondary system ; and if the extent 
or importance of the work should demand it, the secondary 
may be sub-divided into tertiary triangles. 

Having completed the triangulation, the characteristics 
of the surface, such as roads, streams, villages, boundaries, 
&c., are filled in by means of the compass, plain table, or 
some of the methods already explained. 

After the field work is completed, the triangles, when 
regarded as spherical, are reduced by applying the formula 
for spherical excess, hereafter explained, and other neces¬ 
sary corrections, and thus the whole work is plotted upon 
paper. 


174 


ELEMENTS OF SURVEYING. [BOOK II 


PRELIMINARY RECONNOISSANCE AND ESTABLISHMENT OF 

SIGNALS. 

7. Before commencing a trigonometrical survey, an ex¬ 
amination of the entire territory should be made for the 
purpose of selecting a location for the base line, and proper 
points for stations; this examination should be more or 
less elaborate, according to the nature and extent of the 
survey. 

The proper distribution and combination of the trian¬ 
gles, so as to adapt them to the survey in hand, require 
great judgment and care, and but few rules can be given for 
the selection of trigonometrical points. Those points should, 
in general, be chosen in such a manner, that they may be 
distinctly visible from each other, and so that the triangles 
formed, by uniting them, may be as nearly as possible 
equilateral. 

It is easily seen, that a triangle which has an obtuse 
or a very acute angle, will experience a greater change of 
form for a given error, than one which is nearly equilate¬ 
ral ; and since the accuracy of each triangle depends upon 
the preceding ones, it is further evident, that the introduc¬ 
tion of a single ill-conditioned triangle, might vitiate the 
whole survey. Except in extreme cases, no angle, less than 
30°, should be used, and even angles of 30° should not be 
admitted when the locality can be so chosen as to prevent 
it. The base is usually much shorter than the sides of the 
primary triangles; these sides, however, should be increased 
as rapidly as is consistent with the above remarks. 

8. The accompanying diagram will illustrate the man¬ 
ner of increasing the sides without introducing ill-con¬ 
ditioned triangles. Having measured the base AB , and the 
requisite angles, the triangles ABO and ABB , may be de¬ 
termined, and the line D0 computed; with DO as a base, 
the triangles DOE and DOF are formed, and thence EIIF\ 
and EGF 1 in which the sides are much greater than the 
base AB. 


SEC. 1] 


SIGNALS. 


175 



In this manner the sides may be increased to any de¬ 
sirable extent. An ordinary map of the country, or a 
sketch made with the pocket comjDass, will be of material 
assistance in making a proper distribution of the stations. 

9. The stations are marked by signals, which may be 
constructed in a great variety of ways, depending upon the 
locality of the stations, and the lengths of the sides of the 
triangles. 

Sometimes a signal has to be raised above the level of 
the adjacent country, in which case it is constructed of 
timbers, and upon the apex, is placed a vertical staff, bear¬ 
ing a flag. The exact trigonometrical point is determined 
by a plumb-line, suspended from the apex of the signal. 

A temporary signal may be constructed with three or 
four pieces of scantling framed and traced, k 

as shown in the annexed figure, with a short * 

pole projecting from the apex. The plumb 
determines the point B , which is the exact trig¬ 
onometrical point over which the theodolite 
is to be placed. Where the sides of the trian¬ 
gles are not very great, a pole, planted ver¬ 
tically, and surmounted by a flag, will an¬ 
swer as a signal. 

In order to distinguish the different signals, the flags 
which they bear, should be different from each other. 
They may be formed by arranging stripes cf white and 










176 ELEMENTS OF SURVEYING. 'BOOK IV. 

reel, according to some pre-arranged plan, and tire flags of 
tlie different stations should be entered in a book. For 
the purpose of future reference, the trigonometrical point, 
at each station, as i?, should be indicated by a permanent 
mark. If the point falls upon a rock, a hole may be drill¬ 
ed to show the locality; or if not, a mark-stone may be 
sunk under the point, deep enough to be beyond the reach 
of accident. A record of the monument should be pre¬ 
served, together with its reference to some of the perma¬ 
nent objects in the neighborhood. 

In order to render the signals visible from the distant 
stations, polished tin plates are sometimes attached to the 
signal-post, so as to reflect the sun towards the stations at 
certain hours of the day. The Drummond-light has also 
been used to show very distant stations. A light may also 
be produced that can be seen at a distance of 60 or 70 
miles, by placing a ball of lime about a quarter of an inch 
in diameter, in the focus of a parabolic reflector, and heat¬ 
ing it intensely by a stream of oxygen gas, directed by a 
blow-pipe, through a flame of alcohol. If obstacles, as trees, 
and under-brush intervene, vistas have to be opened along 
the lines, from station to station. 

MEASUREMENT OF A BASE LINE. 

10. The measurement of a base line on which the ac 
curacy of the entire survey depends, is one of the most 
difficult operations of geodesic surveying, and one, for the 
successful accomplishment of which, art and science have 
been strongly taxed. The selection of a proper site for a 
base line, forms one of the first objects of the preliminary 
reconnaissance. It should, if possible, be fixed on an open 
plain. It must be so chosen, that the surrounding signals 
may be distinctly seen from its extreme points; and hence, 
those signals which mark points of the adjacent triangula 
tion, should be selected with reference to the base. The 
length of the base , should, in a measure, depend upon the 
magnitude of the survey, though circumstances seldom 
admit its being taken more than 6 or 8 miles in length- 


SEC. 1] 


BASE LINE. 


177 


11. Different instruments have been used for measuring 
base lines, such as steel chains, glass, platinum and deal 
rods; and more recently, a combination of rods, of differ¬ 
ent metals, so adjusted, that the apparatus maintains an in¬ 
variable length at all temperatures. This last mentioned 
apparatus, has been much improved, and most successfully 
used by Prof. Bache, in the Survey of the United States 
Coast. 

12. In minor surveys, where the base line does not 
much exceed 1000 or 2000 feet, sufficient accuracy may be 
attained by the use of wooden rods. To render the rods 
less susceptible of change, from moisture, they should be 
saturated with boiling oil, and covered with a thick coat¬ 
ing of varnish. 

The ends of the rods should be protected by metallic 
caps, which prevent their wearing, and insure a more per¬ 
fect contact. 

When the rods are prepared for use, they should be 
carefully compared with some standard measure, and from 
time to time this comparison should be repeated, in order 
to detect any minute change of length, should such change 
take place. 4 

13. The following method of measuring a base line of 
1000 or 2000 feet, may be rendered very accurate. 

Having decided upon the direction of the base, and 
measured it carefully, two or three times with a chain, let 
a theodolite be planted at one end of the line, and direct¬ 
ed upon a flag, planted at the other. Then, by means of 
the vertical limb, let a row of pickets be driven along the 
base, taking care to plant them at a distance from each 
other, equal to the length of one of the deal rods. Then, 
plant in the place of each picket, a vertical post, 6 or 8 
inches in diameter, and projecting a sufficient distance 
above the surface of the ground. If necessary, let the 
posts be steadied by heaping about them, earth or stones. 
Next, with the assistance of a spirit-level, let each post be 
sawed off, so as to bring their tops to the same licrizontal 

12 


178 


ELEMENTS OF SURVEYING. [BOOK IV 


plane, and by means of the theodolite, let a line be marked 
on the top of each post, in the direction of the base. 
This line will determine the direction in which the rods 
are to be placed, and the contact of the ends must all be 
on this line. 

The contact of the rods should be made with great care, 
so as to avoid moving the rod already established; and 
this will be more readily done, when three rods are used. 
The measurement should be repeated two or three times 
to guard against error. 

14. If the nature of the ground does not admit of the 
posts being brought to a level, let them, by means of the 
theodolite, be brought into an oblique plane AB , and aftei 


B 



having measured, as before, the line AB y determine accu¬ 
rately the difference of level between the points A and B , 
equal to BC: then, from the right-angled triangle ABC, we 
should find the horizontal distance AC = VA]f — BC ". 

15. In very extensive surveys, the base should be several 
miles in length, and the apparatus for measurement, as well 
as the operations on the field, become more complicated. 
For a full description of a very perfect base apparatus, and 
the method of using it, the reader is referred to Prof. 
Baclie’s pamphlet, on the subject—the details of the descrip¬ 
tion would exceed our limits. 

TRIANGULATION. 

16. The theodolite is generally used for measuring the 
angles of a trigonometric survey. The extent of the survey, 
and the standard of accuracy to which the results are re¬ 
quired to conform, must determine the size and perfection 
of the instrument to be employed. The angles of the pri¬ 
mary triangles of the United States Coast Survey, are meas¬ 
ured with theodolites, whose horizontal circles are 24 or 30 










SEC. Lj 


TRI ANGULATION 


179 


inches in diameter; and to eliminate ?<s much as possible, 
every source of error, great numbers of operations are made 
on each station, the readings being made on different points 
ot the arc. Usually from 40 to 60 observations are made 
for each angle—one measurement, with the telescope direct, 
and one with it reverted, constituting a complete observa 
tion. With these precautions, it has been found that the 
error in a primary triangle (where the sum of its three an¬ 
gles has been compared with 180°), has fallen much with¬ 
in 3 seconds. The error of 3 seconds has been adopted as 
the highest admissible limit of error. 

17. Observations are also made at the principal stations 
upon the pole-star, and other stars near the pole, for the 
purpose of determining the angle, made by the sides of the 
triangle with the meridian. In minor surveys, and in a 
secondary triangulation, the operations are much less elabo¬ 
rate ; still, every precaution is to be taken to insure the 
greatest attainable accuracy. As a general rule, all the an¬ 
gles of every triangle, should be measured, if possible. 

18. To illustrate the manner of carrying on a minor 
triangulation, let us refer to the plan of the harbor [plate 
6], in which AB is the measured base, (7, D, A, &c., tri¬ 
angulation points, at which signals have been erected. 
Commence the triangulation at A, the west end of the 
base; and for convenience in plotting, it would be well 
to make the line, passing through the 0 point, and 180° 
parallel, in each position of the instrument, to the base 
AB. Having brought the 0 of the vernier to the 0 of the 
limb, clamp the vernier plate, and direct the upper teles¬ 
cope to the signal at B, and clamp the limb. Enter the 
observation as in the following table: 

OBSERVATION AT STATION A. 


i Name of Station, 
i 

Vernier I. 

Vernier II. 

Mean. 

Station B 

00° 00' 00" 

00' 00" 

o 

o 

o 

O 

o 

o 

o 

'x* 

j Station E 

72° 24' 55" 

25' 5" 

72° 25' 00' 

| Station G- 

138° 34' 56" 

35' 4" 

138° 35' 00' 

L *»• 

&c. 

&c. 

&c. 













180 • ELEMENTS OF SURVEYING. [ROOK IT 

Having recorded tlie reading of the first vernier, and 
the minutes and seconds of the second vernier, unclamp 
the vernier plate, and direct the telescope to the station at 
E) and record both verniers, as before. Again unclamp the 
vernier plate, and direct the telescope on the signal at G ; 
and then read and record, as before. 

Having determined the angles subtended by all the 
signals visible from A , let the theodolite be removed to 
B. Bring the 0 of the vernier I to 180° on the limb, and 
direct the telescope on the signal at A —the line (0°, 180°) 
will then be parallel to its first position, and the limb may 
be clamped. Head now the angles to the signals at A y E y 
0\ &c., and record as before. 

If the theodolite is now removed to the station E, the 
line (0°, 180°), may be made parallel to its first position, 
by adding 180° to the reading of the first vernier, from A 
to A, and then directing the telescope on the signal at A. 
The line (0°, 180°), will thus be made parallel to AB, and 
the reading may be made and recorded as before; and 
so on until all the stations have been visited, and the an¬ 
gles measured. From the field records, the angles BAE y 
EAG , ABE\ EBG , &c., may be easily deduced, the whole 
may be plotted on paper, or the several sides may be com¬ 
puted trigonometrically. It may be observed that the line 
(0°, 180°), has been made parallel to the base line at each 
station; where great accuracy is required, this cannot be 
done, since a single reading is insufficient to give the angle. 
The angle is then determined, as directed in the previous 
article, or by means of the principle of repetition. 

19. To illustrate this principle of repetition, suppose the 
0 of the vernier to coincide with the 0 of the limb, and the 
telescope to be directed, from the station A, upon one of the 
objects, as the signal at B. Clamp the limb, and unciamp- 
ing the vernier plate, direct the telescope on the second ob 
ject, as the signal at E. If we now clamp the vernier 
plate, and unclamping the limb, direct the telescope on the 
signal at B , the line (0 3 , 180°), of the limb, will make 
with AB, an angle equal to BAE. Again clamp the limb, 


SEC. I] 


TRIANGULATION. 


181 


and unclamping the vernier plate, direct the telescope on 
the signal at E. The reading will evidently be equal to 
twice the angle BAE J and if we repeat the operation, the 
reading will be three times the angle, and so on. After 
ten repetitions, if we add 360° each time the 0 of the 
vernier passes the 0 of the limb, the final reading will be 
ten times the angle BAE 1 affected with the joint errors or 
the ten observations, and one-tenth of this will be the read¬ 
ing required, to a greater degree of accuracy than could 
probably be attained by a single observation. 

20. The method of reading angles, by this mode, is as 
follows: 

Angles at station A, between signals B (left), and E 
(right.) 

June 8th, 1851. 


No. of Repe¬ 
titions. 

Vernier I. 

Vernier 

II. 

Mean of Verniers. 


1 

72° 24' 55" 

25' 5" 

72° 25' 00" 


2 

144° 49' 55" 

50' 0" 

144° 49' 58" 


3 

217° 14' 50'' 

15' 10" 

217° 15' 00" 


4 

289° 39' 50" 

40' 00" 

289° 39' 55" 

4)289 : 'S9'55" 




Mean reading 

72° 24' 59" 


FILLING UP THE SURVEY. 

21. After the triangulation is completed, the interior 
may be filled up by the aid of the Compass, or the plane- 
table. 


USE OF THE COMPASS. 

22. When the secondary and tertiary triangles have been 
considerably multiplied, the compass is taken in hand. 
The field-notes may be kept in the following manner. Di¬ 
vide a page of the note-book into two equal parts, by two 
parallel lines near to each other, and consider each part as 
a separate leaf or page. Each leaf is divided into three 

















182 


ELEMENTS OF SURVEYING. [BOOK IV 


spaces, and the middle space is generally smaller than either 
of the others, which are equal. 

The notes begin at the bottom of the first page, and 
run up the page to the top. They then commence again 
at the bottom of the next page, and run up to the top; 
thence to the bottom of the third page, and thus, for as 
many pages as the work may require. 

When the compass is used in the way we are about to 
explain, the distances to objects which lie on the right or 
left of the courses, are determined by means of offsets. 

The beginning of every course is designated in the mid¬ 
dle column by 0, and the bearing is entered directly above. 
The other figures of the middle column, express the dis¬ 
tances from the beginning of each course to the offsets, and 
those in the side columns indicate the lengths of the offsets, 
or the distances to objects on the right or left of the com¬ 
pass lines. 

To explain more definitely the manner of using the 
compass on the field, let us suppose that we have deter¬ 
mined the prominent points and longer lines with the 
theodolite. Place the compass at A (Plate 6), and take the 
bearing of the line AE\ which is S 12° W. 



Enter this bearing at A. Then measure along the line 


































SEC. I.] 


THE PLANE-TABLE. 


183 


AE any distance, as Aa equal to 130 yards, and make an 
offset to the lake, which we measure and find to be 50 
yards. Enter the 130 in the middle column, and as the 
lake lies on the right (in going from A to E), we insert 
the 50 in the right hand column. 

We then measure along the line AE to &, 350 yards 
from A, Here we make a second offset to the lake, and 
find it to be equal to 100 yards. Having entered the dis¬ 
tances in the notes, we measure to g, the point where the line 
AE crosses the creek, and we enter the distance from A, 
415 yards. 

At d , we lay off an offset on the left, to the pond, 70 
yards: at e , an offset to the mouth of the creek, 150 yards: 
and at A, where the course terminates, an offset to the 
lake, of 160 yards. The entire distance from A to A is 
800 yards. 

At A, we take the bearing to E, which is 1ST 50° E. 
Having measured along this line to f 315 yards, we make 
an offset to the pond, on the left, of 50 yards, and to the 
shore, on the right, of 90 yards. Having entered these 
distances, we recommence the notes at 315 below, which we 
sappose to be at the bottom of the second page. Having 
reached H, the extremity of the course, we enter the en¬ 
tire distance from A, 680 yards. We next take the bear¬ 
ing to S 52° E. We then measure the distances to wi, 
n , jp, and I, and enter them, together with the offsets, as 
in the notes. 

23. It is also well to make, in the columns on the right 
and left, such sketches of the ground, fields, houses, creeks 
and rivers, as will afford the means of making an accu¬ 
rate delineation on paper. 

THE PLANE-TABLE—ITS USES. 

24. PI. 3, Fig. 1. The plane-table consists of two parts; 
a rectangular board CDBA , and a tripod EHG , to which 
it is firmly secured. 

Directly under the rectangular board are four milled 
screws which pass through sockets inserted in a horizontal 


184 


ELEMENTS OF SURVEYING. [BOOK IV 


brass plate : these screws are worked against a second ho¬ 
rizontal plate, for the purpose of levelling the table; the 
table having a ball and socket motion, similar to the limb 
of the theodolite. 

For the purpose of levelling the table, a small detached 
spirit-level is used. This level being placed over the 
centre, and also over two of the levelling screws, the screws 
are turned contrary ways until the level is horizontal; 
after which, it is placed over the other two screws, and 
made horizontal in the same manner. 

Between the upper horizontal plate and the table, there 
is a clamp-screw, similar to the clamp-screw of the theodo¬ 
lite, which being loosened, the table can be turned freely 
about its axis. There is, also, a small tangent-screw, by 
which the smaller motions of the table are regulated, after 
the clamp-screw is made fast. Neither of these screws can 
be seen in the figure. 

The upper side of the table is bordered by four brass 
plates, about one inch in width, and the centre of the table 
is marked by a small pin, F. About this centre, and tan¬ 
gent to the sides of the table, conceive a circle to be de¬ 
scribed. Suppose the circumference of the circle to be di¬ 
vided into degrees and parts of a degree, and radii to be 
drawn through the centre and the points of division. The 
points in which these radii intersect the outer edge of the 
brass border, are marked by lines on the brass plates, and 
the degrees are numbered in the direction from left to 
right, from the point L to the point 180°, and from the 
point / to the point A, 180°. In some plane-tables, how¬ 
ever, they are numbered from 0 to 360°. 

There are, generally, diagonal scales of equal parts cut 
on the plates DLC and AZZ>, the use of which will be ex¬ 
plained hereafter. 

Near the two other edges of the table, two small grooves 
are made, into which the plates of brass DB and CA are 
fitted, and these plates are drawn to their places by means 
of milled screws, which pass through the tab'e from the 
under side, and screw firmly into the plates. The heads 


SEC. I.] 


THE PLANE-TABLE. 


185 


of two of the screws, Q and S ) are seen in the figure, as 
also one of the plates and its two screws in Fig. 3. The 
object of these plates is to confine a sheet of paper on the 
table. By loosening the screws, and pressing them up¬ 
wards, the plates are raised above the surface of the table; 
the edges of the paper can then be placed under them: 
then, by turning the screws back again, the plates are 
drawn down and the paper held tightly. Fig. 1 represents 
the table with the paper partly put upon it: one edge of 
the paper has been placed under the plate BB , and the 
screws S and Q , tightened. The paper, before being put 
on, should be moistened, in order to expand it; and then, 
after it has been dried, it will fit closely to the table. 

A ruler, AB (Fig. 2), with open vertical sights, is used 
with the plane-table. This ruler has a fiducial edge, which 
is in the same vertical plane with the hairs of the sights. 
A ruler with a telescope, and a vertical limb, similar to the 
vertical limb of the theodolite, is sometimes used with the 
plane-table. A compass, also, is often attached to the table, 
to show the bearings of the lines. 

The plane-table is used for two distinct objects. 

1st. For the measurement of horizontal angles. 

2dly. For the determination of the shorter lines of a 
survey, both in extent and position. 

TO MEASURE A HORIZONTAL ANGLE. 

25. Place, by means of a plumb, the centre of the table 
directly over the angular point: then level the table; after 
which, place the fiducial edge of the ruler against the small 
pin at the centre : direct the sights to one of the objects, 
and note the degrees on the brass plate ; then turn the 
ruler and sights to the other object, and note the degrees 
as before. If the ruler has not passed over the 0 point, 
the difference of the readings is the angle sought; but, if 
it has, the larger taken from 180°, and the remainder added 
to the smaller, gives the required angle. 

TO DETERMINE LINES IN EXTENT AND POSITION. 

26. Having placed a paper on the table, examine 


L86 ELEMENTS OF SURVEYING. (BOOK IV 

objects and lines which are to be determined, and select 
for a base a convenient portion of such a line of those 
already formed in the triangulation, that most of the ob¬ 
jects can be seen from its extremities. Then place the 
plane-table with its centre, nearly, though not accurately 
over one extremity of the base; make it truly horizontal, 
and turn it until the larger part of the paper lies on tho 
same side of the base with the objects. 

Then, tighten the clamp-screw, and mark with a pin tho 
point of the paper directly over the station, which point is 
determined most accurately by suspending a plumb from 
the lower side of the table. Press the pin firmly on this 
point, bring the fiducial edge of the ruler against it, and 
sight to the other extremity of the base line, and mark 
with the pin or pencil, the direction of the line on the 
paper. Sight in like manner to every other object, and 
draw on the paper the corresponding lines, numbering them 
from the base line, 1, 2, 3, 4, &c. 

Then, with a pair of dividers, take from the scale a 
certain number of equal parts to represent the base, and 
lay off the distance on the base line from the place of the 
pin. Take up the table, carry it to the other extremity 
of the base, and place the point of the paper correspond¬ 
ing to that extremity, directly over it. Place the fiducial 
edge of the ruler on the base line, and turn the table, by 
means of the tangent-screw, until the sights are directed to 
the first station. If, however, in bringing the table to this 
position, the corresponding point of the paper has been 
moved from over the extremity of the base line, move the 
legs of the tripod until it is brought back to its place. 
Let the table be then levelled, after which, place the ruler 
again on the base line, and bring the table to its proper 
position by the tangent-screw, and continue the adjustment 
until the extremity of the base line on the paper is directly 
over the station, and in the same vertical plane with the 
base line on the ground. Then direct the sights to all the 
objects sighted to from the other station, and mark the 
lines 1, 2, 3, 4, &c., from the base line, as before. The 
intersections of the corresponding lines 1,1, 2,2, 3,3, 4,4, 


SEC. I.J 


THB PLANE-TABLE 


187 


&c., determine, on the paper, the positions of the several 
objects; and a reference of these lines to the scale of equal 
parts, determines the true distances. 



27. Let it he required, for 
example, to determine, by 
means of the plane-table, the 
relative positions of several 
houses. 

v From station A, and on 
one of the lines of the tri¬ 
angulation, as AB , measure 
the base line AN, which we will suppose equal to 300 
yards. Place the plain-table at A, and sight to the corners 
of the houses, and mark the lines 1, 2, 3, 4, &c. Then 
remove the table to N, and sight to the same corners as be¬ 
fore, and draw the lines as in the figure. The points at 
which they intersect the corresponding lines before drawn, 
determine the corners of the houses. The front lines of 
the houses may then be drawn on the paper. Draw lines 
at right angles to the front lines, and on them lay off the 
depths of the houses, with the same scale as that used for 
the base line. 


To find the length of any line drawn on the paper, as 
the line 1, drawn through A, for example, place the divi¬ 
ders at A and extend them to the other extremity of the 
line, and then apply the line to the scale. The length of 
the line 1 is equal to 198 yards. 


28. In this example, we de¬ 
termine from the base line 
CD, the positions of the points 
F, E\ and H. 



OF CHANGING THE PAPER. 

29. When one paper :s filled, and there is yet more 
work to be done, let the paper be removed, and a second 
paper put on the table; after which, the table may be 
used as before. 







188 


ELEMENTS OF SURVEYING. [B( Oa IV 


Now, in order tliat the two papers may be put toge¬ 
ther and form one entire plan, it is necessary that two 
points determined on the first paper, be also determined 
on the second; and then, by placing the lines joining 
these points, one on the other, all the lines on the two 
papers will have the same relative position as the corres¬ 
ponding lines on the ground; and the same for as many 
papers as it may be necessaiy to use. If different scales 
are used, the corresponding points will not join, and then 
the work must be reduced to the same scale, before the 
papers can be put together. 

In the first example, the position of the point F was de¬ 
termined, in order to unite the first paper with the second. 

In the second example, we sighted from C and D, the 
extremities of the base line, to the points N and F ; we 
thus determined the line NF on the second paper. Pla¬ 
cing the line NF of the one paper on NF of the other, we 
have the following plan. 



In this plan, all the points and lines are accurately laid 
down. Any number of papers may be joined in the same 
manner. 

80. The principal use of the plane-table is for the in¬ 
terior filling up of trigonometrical surveys; it is also used 
with advantage, when only a plot of a field is wanted. 

It ought not be used for the determination of long lines, 
nor can it be relied on for determining extended areas. 

Having finished the field-work, some corrections are ne- 
cessary, before plotting the survey. The principal correc¬ 
tions are, the reduction to the centre of the station, and 
the correction for spherical excess. 




SEC I.] 


CORRECTIONS. 


189 


REDUCTION TO THE CENTRE. 

31. It sometimes happens that fixed objects, as steeples, 
towers, and the like, are nsed instead of signals, in a sur¬ 
vey. The theodolite cannot be placed over the centre of 
such stations. In all such cases, the instrument must be 
planted as near as possible to the station; then the angles, 
subtended by the various objects being measured, the true 
angle subtended at the centre of the station, is computed 
by the following formula. 

Suppose A , B and C,\ to be 
the three stations. Let us sup¬ 
pose that the theodolite cannot 
be placed over (7, but that it 
can be placed at j D, a point 
near C. 

Let the angles ABB and ABC be 
measured; also the distance (2D, and 
the distances AC and BO computed, 
approximatively, from the side AB and 
the angles A and B. The true angle 
ACB may then be found. 

For, ABB = ACB + CAB (Geom., Bk. L, Prop. 25, C. 6): 
and ABB = ABB + BBC : 

hence, by equating the equal values, 

ACB+ CAB = ABB + BBC\ 


or, 


ACB— ABB + BBC - CAB . 

But, 

BC 

: CB : : sin BBC : sin BBC; 
CB 

or, 


sin BBC — sin BBC : 

and 

AC 

: CB : : sin ABC : sin CAB; 
CB 

or, 


sin CAB— , n sin ABC. 

AC 


Hence, by substitution, we have 

/ CB . CB . 

A CB = ABB + y jjq sin BBC- sin ABC); 

for, since the distance BC is very small in comparison with 
BC and AC,\ the angles BBC and CAB are very small; 
and hence, their sines may be substituted for the angles 
themselves. 


A B 



C D 






190 ELEMENTS OF SURVEYING. [BOOK IY 

It is to be observed, that when the radius is unity, in 
the above formula, the natural sines of the angles are used, 
and that the correction within the parenthesis, is expressed 
in linear units, and will be positive or negative, according 
as the second term is less or greater than the first. 

To convert the linear correction into seconds of an arc, 
whose radius is unity, let the deduced correction, within 
the parenthesis, be denoted by c. Then, since the radius 
is 1, we shall have 

length of semi-circumference 
: the linear correction 
: : the number of seconds in 180° 

: the number of seconds in the correction: 
that is, denoting the number of seconds in the correction 
by n, 

3.1416 : c :: 648000" : n ; or n = c X 206264.3" : 

c will, in all cases, be a very small fraction. 

This correction is not often necessary, for in extensive 
operations, such stations are chosen as will allow of the 
measurement of all the angles, and in secondary triangles, it 
is admissible to measure only two of the angles. 

% 

SPHERICAL EXCESS. 

0 

32. It has already been noticed, that the triangles meas¬ 
ured, are on the surface of a sphere, and consequently, the 
angles taken between any three points, by a theodolite, are, 
strictly speaking, the angles of a spherical triangle; hence, 
the sum must exceed 180°, (Geom., Bk. IX., P. 14). This ex¬ 
cess is called the spherical excess. In the processes of trian¬ 
gulation, we reduce all triangles to rectilineal triangles; and 
hence, the sides of the triangle, which we seek, are chords 
of the sphere, and not arcs measured on the surface. 

33. In small triangles, where the sides do not exceed 
6 or 8 miles, the spherical excess may be altogether ne¬ 
glected; but in large triangles, it must be taken into ac¬ 
count. Of all the methods, yet known, of correcting for 
the spherical excess, Legendre’s is considered the best. 



SEC. I.] 


SPHERICAL EXCESS. 


191 


This method is based upon the proposition that, the area 
of a spherical triangle , which is very small when compared 
with the entire surface of the sphere , is nearly identical with a 
rectilineal triangle , whose sides are of the same length as those 
of the spherical triangle , and whose angles are each diminished 
by one-third of the spherical excess. 

34. The first thing, then, is to find the spherical ex¬ 
cess, and for this, we must know the area of the triangle. 
The rules for determining the area of the rectilineal trian¬ 
gles, will afford results sufficiently near, and the first ap¬ 
proximate area may be computed in square feet, as though 
the triangle were rectilineal. Having found this area, the 
formula of Legendre, gives the logarithm of the spherical 
excess, estimated in seconds, equal to the logarithm of the 
area of the triangle computed in square feet, minus the 
constant logarithm 9.326770. That is, if we put 

E = the spherical excess, in seconds. 

A = area of the triangle, in square feet. 

Constant log. = 9.326770; 

we shall have, 

Log E — log A — 9.326770. 

Having found the spherical excess, we divide it by 3, 
and then diminish each angle of the triangle by the quo¬ 
tient ; the sum of the three angles should then be equal to 
180°. With these new angles, we compute all the parts of 
the triangle. 

35. The spherical excess between latitude 25° and 45°, 
is about 1" for an area of 75.5 miles; hence, to obtain a 
close approximation to the spherical excess, divide the num¬ 
ber of square miles in the area of the triangle by 75.5, the 
quotient will be the number of seconds required. 

36 To find the spherical excess, knowing the two sides 
a and b, and the included angle C. 

a b sin C. 


area = 



192 


ELEMENTS OF SURVEYING. [BOOK IV 


Suppose ci — 248230 feet, b — 212628 feet, and C 103 
19' 10". 

a. 248230 .log- 5.394854 

b . 212628 .log_ 5.327620 

G . . 103° 19' 10" . . . log sine . . . 9.988158 

ar. comp, of 2, diminished by 10 . . 1.698970 

20.409602 

Log of R.10. 

Log A. 10.409602 

Constant logarithm .... 9.326770 

Hence, E =12.1" . 1.082832. The sum of 

the three measured angles ought therefore to exceed 180°, 
by this amount. The angles being corrected, by subtract¬ 
ing 4.J" from each, the parts of the triangle may be com¬ 
puted, by regarding the sides as rectilineal. 

PLOTTING THE TRIANGULATION. 

87. The sides of the triangles being computed, after 
having made the necessary corrections, the work may then 
be plotted, as already explained, either by means of the 
circular protractor, or by the method of chords. 

THE CIRCULAR PROTRACTOR. 

I 

38. This instrument consists of a brass circular limb 
(PI. 2, Fig. 4), of about six inches in diameter, with a 
movable index AB, having a vernier at one extremity A ) 
and a milled screw at the other extremity B , with a con¬ 
cealed cog-wheel that works with the cogs of the limb, and 
thus moves the index AB about the centre of the pro¬ 
tractor. At the centre of the protractor is a small circular 
glass plate, on which two lines are cut; the point of their 
intersection, is the exact centre of the instrument. The 
limb is generally divided to half degrees; the degrees are 
numbered from 0 to 360. 

At the 0 point, and at the opposite extremities of the 
diameter passing through that point, are small lines on the 
inner edge of the limb; the two extremities of the diam- 












OF PLOTTING. 


SEC. L] 


193 


eter, perpendicular to this latter, are designated in the same 
way. 

Two angular pieces of brass, each having a small and 
sharp steel pin at its extremity, are fastened to the index, 
and revolve freely around the lines ab and cd. The small 
screws, a, b , c, and d , move them in the directions of the 
lines ab , cd , for the purpose of bringing the steel pins ex¬ 
actly into the line which passes through the 0 of the in¬ 
dex and the centre of the protractor. 

To adjust them to their places, place the centre of the 
protractor over a marked point, and the 0 of the index to 
the 0 of the limb. Then mark the place of the index by 
the pins: after which, turn the index 180°, and see if the 
pins will mark the same points as before. If they do, the 
index is adjusted; if they do not, correct the error with the 
screws a, 5, c, and d. 

TO LAY OFF AN ANGLE WITH THE PROTRACTOR. 

39. Let its centre be placed over the angular point, and 
the diameter passing through 0 and 180°, on the given line. 
Turn the screw that works the index, until the 0 of the 
vernier coincides with the division corresponding to the 
given angle; then let the angular brass pieces be turned 
down; the points dotted by the steel pins will show the 
direction of the required line. 

If this line does not pass through the angular point, 
the pins are out of place, and must be adjusted. 


FIRST METHOD OF PLOTTING. 

40. Suppose it were required to make the plan of the 
harbor on a scale of 450 yards to an inch. 

Divide the length of the base line AB , which we will 
suppose equal to 1140 yards, by 450, and the quotient 2.53 
will express the length which is to represent the base line 
on the paper (Bk. I., Art. 54.) 

Draw an indefinite line AB, to represent the base, and 
having chosen any point, as A, for the first station, lay off 
2.53 inches to B. The other extremity of the base line 
will thus be determined. 

13 


194 ELEMENTS OF SURVEYING. [BOOK IV 

Then, place the circular protractor at A , and lay off 
the angle BAE\ and then the angle EAG. Next, place 
the protractor at B , and lay off the angles ABE and EBO. 
The intersection of the lines AE and BE will determine 
the station E. Let the protractor be then placed at this 
point, and all the angles of station E, laid down. 

The point G, where EG intersects AG, and the point 
G,\ where EC intersects BC\ will then be found. 

By placing the protractor at C and G , we can deter¬ 
mine the points D and F\ when the place, on the paper, of 
all the stations will be known. 

To unite the work done with the compass, spread the 
compass-notes before you, and draw through A a line to 
represent the meridian. This line makes an angle of 12° 
with the course AE. 

Then, lay off from the scale the distances Aa, Ab, Aq , 
Ac, Acl, Ae , and at the several points erect perpendiculars 
to AE. Lay off on these perpendiculars the lengths of the 
offsets, and the curve traced through the points so deter 
mined, will be the margin of the lake. 

At E, draw a parallel to the meridian through A , and 
lay down the course EH, which makes an angle of 50° with 
the meridian. Then, lay down the several distances to the 
offsets, and draw the offsets and lay off their lengths. Do 
the same for the course HI, and all the compass-work will 
be plotted. 

The work done with the plane-table (Art. 28), is united 
to the work done with the theodolite, by simply placing 
the line AN on the paper of the plain-table, upon the line 
AN, drawn on the plot of the triangulation. 

SECOND METHOD OF PLOTTING. 

41. Place the centre of the protractor near the centre 
of the paper, and draw a line through the points 0 and 
180°. This line will have the same position with the cir¬ 
cular protractor that the base line AB had with the limb 
of the theodolite. 


SEC. LJ 


METHOD OF CHORDS 


195 


Lay oil then from the 0 point an arc equal to the 4irec- 
fcion from A to E, also an arc equal to the direction AG 
and through the centre point, and the points so determined, 
draw lines. Lay off in succession, in a similar manner 
the directions taken at all the stations; and through the 
centre point, and the points so determined, draw lines, and 
designate each by the letters of the direction to which it 
corresponds. 

Now, since all the lines drawn on the paper have the same 
position with the circular protractor, as the corresponding 
lines on the ground have with the limb of the theodolite, 
it follows that each direction will be parallel to its corres¬ 
ponding line upon the ground. 

Hence, any line may be drawn parallel to that passing 
through 0 and 180°, to represent the base line AB. Having 
drawn such a line, and marked a point for the station A, 
lay off the length of the base, and the extremity will be 
the station B. 

Through A and B, so determined, draw parallels re¬ 
spectively to the lines corresponding to the directions AB 
and BE ' and the point of intersection will determine station 
E Through B and E draw parallels to the lines which 
correspond to the directions BC, CE , and their point of 
intersection will determine station C. Through G and E 
draw lines parallel to the lines corresponding to the direc¬ 
tions CE and ED, and the point of intersection will de¬ 
termine D. In a similar manner we may determine the 
stations F and G. 

METHOD OF CHORDS. 

42. Let us first prove that the chord of a given arc is 
equal to the sine of half the arc ivith double the radius. 

Let DAF be any given angle, 
and AH a line bisecting it. Let 
DC be the chord of the arc CD, 
described with a given radius, 
and 11F parallel to CD, the sine 
of half the given angle, to a radius AF~ 2 AC. 





196 


ELEMENTS OF SURVEYING. [BOOK IV 


Since AF—2AC we have, from similar triangles, HF~ 
2KC, but DC=2KC, hence EF— CD. 


TO LAY OFF AN ANGLE. 


43. To avoid, as far as possible, 
the use of fractions, let us suppose 
the radius of the table of natural 
sines to be 1 ten , or 10 inches. 

Take from a scale 5 equal parts, 
with which as a radius, from the centre A , describe an 
arc CD. Take from the table the natural sine of half 
the arc, and remove the decimal point one place to the 
right; the result will express the sine of half the arc to the 
radius 10, or the chord of the arc to the radius 5. From 
the same scale, take this sine in the dividers, and from (7, 
as a centre, describe an arc cutting CD in D\ draw AD, 
and CAD will be the angle required. 



90 ° 


This is the most accurate of all the methods of laying 
off an angle, and it may also be applied advantageously to 
the second method of plotting, thus: 

Draw a fine straight line, generally 
in the direction of the meridian or of 
the base line of the survey; and also 
a line exactly perpendicular to it. From 
the point of intersection, as a centre, 
with a radius of 5 equal parts of the 
scale, describe the circumference of a 
circle cutting the straight lines in the points marked 0 
and 90°. 



To lay off an angle, as for instance, the angle 14° 29 f . 
The half of it is 7° 14' 30", the natural sine of which is 
0.126005, or 1.26 to the radius of 10 inches. Set off from 
0 to 5, as in the figure, this distance taken from the scale, 
and through the two points 5, &, thus determined, draw a 
straight line. This line should pass through the centre, 
and will make with the line (0, 0) the angle 14° 29'; and 
any line on the paper drawn parallel to it, will make with 

the line (0, 0) the same angle. The further application is 
obvious 






SEC. XL] 


MARITIME SURVEYING. 


197 


SECTION II. 

MARITIME SURVEFING. 

44. When, in connection with a trigonometrical survey 
on shore, a harbor is to be surveyed for the purpose of 
ascertaining the channels, their depth and width, the posi¬ 
tions of shoals, and the depth of water thereon, other 
means must be used, and other examinations made in ad¬ 
dition to those already referred to. 

Let buoys be anchored on the principal shoals and along 
the edges of the channel, and using any one of the lines 
already determined as a base, let the angles subtended by 
lines drawn from its extremities, to the buoys respectively, 
be measured with the theodolite. Then, there will be 
known in each triangle the base and angles at the base, 
from which the distances to the buoys are easily found ; 
and hence, their positions become known. 

Having made the soundings, and ascertained the exact 
depth of the water at each of the buoys, several points of 
the harbor are established, at which the precise depth of 
the water is known; and by increasing the number of the 
buoys, the depth of the water can be found at as many 
points as may be deemed necessary. 

45. If a person with a theodolite, or with any other in¬ 
strument adapted to the measurement of horizontal angles, 
be stationed at each extremity of the base line, it will not 
be necessary to establish buoys. A boat, provided with 
an anchor, a sounding line, and a signal flag, has only to 
throw its anchor, hoist its signal flag, and make the sound¬ 
ing, while the persons at the extremities of the base line 
measure the angles;—from these data, the precise place oi 
the boat can be determined. 

46. There is another method of determining the places 
at which the soundings are made, that admits of great 


198 


ELEMENTS OF SURVEYING. [BOOK IT 


despatch, and which, if the observations are made with 
care, affords results sufficiently accurate. 

Having established, trigonometrically, three points which 
can be seen from all parts of the harbor, and having pro 
vided a sextant, let the sounding be made at any place in 
the harbor, and at the same time the three angles subtend¬ 
ed by lines drawn to the three fixed points, measured with 
the sextant. 

The problem, to find, from these data, the place of the 
boat at the time of the sounding, is the same as example 
(3, page 62. 

It is only necessary to measure two of the angles, but 
it is safest to measure the third also, as it affords a veri¬ 
fication of the work. 

The great rapidity with which angles can be measured 
with the sextant, by one skilled in its use, renders this a 
most expeditious method of sounding and surveying a 
harbor. 

The sextant is not described, nor are its uses explained 
in these Elements, because its construction combines many 
philosophical principles, with which the Surveyor cannot 
be supposed conversant. 

47. There is yet another method of finding the sound¬ 
ings, which, although not as accurate as those already ex¬ 
plained, will, nevertheless, afford results approximating 
nearly to the truth. It is this:—Let a boat be rowed uni¬ 
formly across the harbor, from one extremity to the othei 
of any of the lines determined trigonometrically. Let 
soundings be made continually, and let the precise time of 
making each be carefully noted. Then, knowing the 
length of the entire line, the time spent in passing over it, 
as also the time of making each of the soundings, we can 
easily find the points of the line at which the several 
soundings were made; and hence, the depth of water at 
those points becomes known. 

48. If a person stationed on shore with a theodolite, takes 
the bearing of the boat, at every second or third sounding, 
determined by hoisting a flag, it will fix the positions of the 


8 EC. Il.j 


MARITIME SURVEYING. 


199 


soundings with great accuracy. Soundings may thus be 
made along any number of known lines, and a comparison 
of the depths found on different lines, at or near their 
points of interne ction, will show with what degree of ac¬ 
curacy the work has been done. 

Sounding-lines should be made of strong cord, and di¬ 
vided into feet or fathoms, by different colored rags or 
other marks. The lead is shaped like 
the frustum of a cone, with the base 
B, hollowed out, to hold some grease. 

The land or mud of the bottom adheres 
to the grease, and thus shows the na¬ 
ture of the bottom, which should be en¬ 
tered in the field-book, and laid down 
upon the map. As the cord is liable 
to change its length, it should be com¬ 
pared from time to time with some 
standard. In tideuvaters, the exact time 
of each sounding is to be noticed, and 
an assistant should note the height of the tide at regular in¬ 
tervals, upon a tide-guage. The tide-guage is permanently 
placed at some convenient point of the harbor, and its 0 
point is referred by means of a spirit-level, to some fixed 
bench-mark, on a level with mean low-water mark, to 
which all the soundings must be reduced. 

49. Having plotted the work done with the theodolite, 
as also the outline of the harbor traced with the compass, 
it remains to delineate the bottom of the harbor; and this 
is done by means of horizontal curves, which have already 
been used to represent broken or undulating ground. 

Let the plane of reference be taken through low-water 
mark, or to coincide with the surface of the water at low 
tide. The accuracy with -which the bottom of the harbor 
is to be delineated, will guide us in fixing the distance be¬ 
tween the horizontal planes of section. 

The first horizontal plane should be passed at a dis¬ 
tance below the shallowest point that has been sounded, 
equal to the number of feet fixed upon for the distance 
between the planes of section; and the curve, in which it 



200 


ELEMENTS OF SURVEYING 


[BOOK IV 


intersects the bottom of tbe harbor determined as in Book 
III. Sec. II. And similarly, for the other horizontal planes 
of section. 

Having thus delineated the bottom of the harbor, and 
noted on the map the distance of each intersecting plane 
below the plane of reference, let such lines be drawn as 
will indicate the channels, shoals, sunken rocks, and direc 
tion of the current. 

In the example given in plate 6, soundings have been 
made in three directions from the sand-bar in the harbor. 

I 7 

and also from the rocky shore across to the light-house. 


BOOK V. 

OP NAVIGATION. 


t 


SECTION I. 

DEFINITIONS. 

1. We have given, in the preceding parts of this work, 
various applications of Plane Trigonometry. We propose, 
in this Book to explain the best methods of determining 
the place of a ship at sea. This application of Trigonom¬ 
etry constitutes the science and art of Navigation. 

2. There are two methods of determining the place of 
a ship at sea. 

1st. When a ship departs on her voyage, if we note 
her courses and the distance sailed, we may, at any time, 
by means of Plane Trigonometry, determine her place, very 
nearly. 

2d. By means of observations on the heavenly bodies, 
and the aid of Spherical Trigonometry, we may determine 
with great accuracy, the place of the ship. This method 
is called Nautical Astronomy. 

The first part of Navigation, viz., the cases which can 
be solved without the aid of observations on the heavenly 
bodies, will be alone treated of. 

3. The earth is nearly spherical. For the purposes of 
Navigation it may be considered as perfectly so. It re¬ 
volves round one of its diameters, called the axis , in about 
twenty-four hours. 

4. The great circle, whose poles are the extremities of 
the axis, is called the equator. The poles of the equator 



202 


ELEMENTS OF SURVEYING. [BOOK V 


are called the poles of the earth—one is called the north 
pole, and the other the south pole. 

5. The circumference of every great circle which passes 
through the poles, cuts the equator at right angles, and is 
a meridian circle. Every place on the surface of the earth 
has its own meridian ; but for the purposes of Geography 
and Navigation, all the meridians are reckoned from a par¬ 
ticular meridian, which is called the first meridian. The 
English have fixed on the meridian of the Greenwich Ob¬ 
servatory, for the first meridian. 

6. The longitude of any place is the arc of the equator, 
intercepted between the meridian of that place and the first 
meridian, and is east or west, according as the place lies 
east or west of the first meridian. 

7. The difference of longitude of two places is the arc of 
the equator included between their meridians; this arc is 
equal to the difference of longitudes when they are of the 
same name, and to the sum of the longitudes, when they 
are of different names. 

8. The latitude of a place is its distance from the equator, 
measured on the meridian of the place, and is north or south 
according as the place lies north or south of the equator. 

9. The small circles drawn parallel to the equator, are 
called parallels of latitude. The arc of any meridian inter¬ 
cepted between the parallels passing through any two 
places, measures the difference of latitude of those places; 
this difference is found by subtracting the less latitude from 
the greater, when the latitudes are of the same name, and 
by adding them when they are of different names. 

10. The sensible horizon of any place is an imaginary 
plane, supposed to touch the earth at that place, and to be 
extended indefinitely. 

A plane passing through the centre of the earth, and 
parallel to the sensible horizon, is called the rational horizon. 

The north and south line, is the intersection of the 
plane of the meridian circle with the sensible horizon, and 
the line which is drawn perpendicular to this, is called the 
east and west line. 


SEC I.] 


NAVIGATION. 


203 


11. The course of a ship, at any point, is the angle which 
her track or keel makes with the meridian. So long as the 
course is unchanged, the ship would sail in a straight line, 
if the meridians were truly parallel; but as the meridians 
bend constantly toward the pole, the direction of her path is 
continually changing, and she moves in a. curve called the 
rhumb line. The course of a ship is indicated by the mari¬ 
ner’s compass. 

12. The marin¬ 
er’s compass consists 
of a circular card, 
whose circumfer¬ 
ence is divided into 
thirty-two equal 
parts called points ; 
each point being 
subdivided into four 
parts, called quar¬ 
ter points. 

To the under 
side of this card a 
slender bar of mag¬ 
netized steel, called 
a needle , is permanently attached. The direction of the 
needle corresponds to the diameter NS. The diameter EW, 
at right angles to NS, is intended to indicate the east and 
west points. The points of the compass are thus read: be¬ 
ginning at the north point, and going east, we say, north 
and by east , north north east, north east and by north, 
north east; and so on, round the compass, as indicated by 
the letters. 

The card being permitted to turn freely on the pin, on 
which it is poised, as a centre, the line NS will always 
indicate the true magnetic meridian, but this, as we have 
seen in (Bk. II., Sec. 7-14), is not the true meridian, and 
hence, the variation must always be allowed for. 

On the interior of the compass box, in which the card 
swings, are two marks a and &, which lie in a line passing 
through the centre of the card, and the compass box is so 









204 


ELEMENTS OF SURVEYING. 


[BOOK V 


placed that this line shall be parallel to the keel of the 
ship. Consequently, if b be placed towards the bow of the 
vessel, the point which it marks on the card will show the 
compass course, for the line NS is always on the magnetic 
meridian, and EW is east and west. The course is gene¬ 
rally read to quarter points, and as a quadrant contains 
eight points, each point is equal to 90° — 8 = 11° 15'; and 
a quarter point = 11° 15' -f-4=2° 48' 45". The table of 
Rhumbs, after the Traverse Table, shows the degrees in 
each course, to quarter points. 

13. A ship’s rate of sailing is determined by means of 
an instrument, called the log , and an attached line called 
the log line. The log is a piece of wood in the form of a 
sector of a circle, the rim of which is loaded with lead, so 
that when it is heaved into the sea it assumes a vertical 
position. The log line is so attached as to hold the log 
square against the water, that it may not be drawn, along 
after the ship as the line unwinds from the reel, by the 
ship’s forward motion. 

The time in which the log line unwinds from the reel, 
is noted by a sand-glass, through which the sand passes in 
half a minute; that is, in the one hundred and twentieth part 
of an hour. 

For convenience, the log line is divided into equal parts, 
marked by knots, and each part is equal to the one hun¬ 
dred and twentieth part of a nautical or geographical 
mile*. 

Now, since half a minute is the one hundred and twen¬ 
tieth part of an hour, and each knot indicates the one hun¬ 
dred and twentieth part of a mile, it follows that the num¬ 
ber of knots reeled off while the half minute glass runs out, 
will indicate the rate of the ship’s sailing per hour. 


* A. geographical mile is one minute, or one-sixtieth of a degree, measured on 
the equator. Taking the diameter at 7916 English miles, the geographical mile 
will be about 6079 feet; that is, one-sixth greater than the English mile, which 
is 6280 feet. 





SEC. Ii.] 


PLANE SAILING. 


205 


SECTION II. 

OF PLANE SAILING. 

14. Let tlie diagram 
EPQ represent a por¬ 
tion of the earth’s sur¬ 
face, P the pole, and 
EQ the equator. Let 
AB be any rhumb line, 
or track described by 
a ship in sailing from 
A to B. 

Conceive the path of the ship to be divided into very 
small parts, and through the points of division draw meri¬ 
dians, and also the parallels of latitude b'b , e'e, d'd, e'e , and 
B'B : a series of triangles will thus be formed, but so small 
that each may be considered as a plane triangle. 

In these triangles, the sum of the bases 
Ab' + be' + cd' + de' + ef— AB', 

which is equal to the difference of latitude between the 
points A and B. Also, 

b'b -f“ e'e 4" d'd -f* e'e -f* fB = BB', 

which is equal to the distance that the ship has departed 
from the meridian ABB , and is called the departure in 
sailing from A to B. 

Therefore, the distance sailed, the dif¬ 
ference of latitude made, and the departure , 
may be represented by the hypothenuse, 
the base and perpendicular of a right- 
angled triangle, of which the angle op¬ 
posite the departure is the course. 

When any of the four parts above- 
named are given, the other two can be 
determined. This method of determining 
the place of a ship reduces all the elements to the parts 
of a plane triangle, and hence is called plane sailing. 











206 


'ELEMENTS OF SURVEYING. [BOOK V 


EXAMPLES. 

1. A ship from latitude 47° 30' N. has sailed S. W, by 
S. 98 miles. What latitude is she in, and what departure 
has she made ? 

Let C be the place sailed from, CB 
the meridian, and BCA the course, which 
we find from the table of rhumbs to be 
equal to 33° 45'; then AC will be the dis¬ 
tance sailed, equal to 98 miles. Also, AB 
will be the departure, and CB the differ¬ 
ence of latitude. 

Then by the formulas for the solution 
of right angled triangles, 


As radius ar. c. 

0.000000 

As radius ar. c. 

0.000000 

: cos G 33° 45' 

9.919846 

: sin C 33° 45' 

9.744739 

: : AC 

98 

1.991226 

: : OA 98 

1.991226 

: CB 

81.48 

1.911072 

: AB 54.45 

1.735965 


Latitude left 47° 30' N. 

Dif. lat. = 81.48 miles = 81.48 minutes = 1° 22' S. 


In latitude 46° 08'. 

Departure, 54.45 miles. 

2. A ship sails 24 hours on a direct course, from lat¬ 
itude 88° 32' N. till she arrives at latitude 36° 56' N. 
The course is between S. and E. and the rate 5j miles an 
hour. Required the course, distance, and departure. 

Lat. left 38° 32' 1ST. 24 X 5J = 132 miles = distance. 
In lat. 36°' 56' 

Diff. 1° 36' = 96 miles. 



As dist. 132 ar. c. 7.879426 
diff. lat. 96 1.982271 

: : radius 10.000000 


As radius ar. c. 0.000000 
: dist. 132 2.120574 

:: sin course 43° 20' 9.836477 



: cos course 43° 20' 9.861697 


90.58 1.957051 


















SEC. Ill] 


TRAVERSE SAILING. 


207 

Hence, the course is S. 43° 20' E., and tlic departure 
90.58 miles east. 

3. A ship sails from latitude 3° 52' S. to latitude 4° 30 f 
K, the course being N. W. by W. h\V. : required the dist¬ 
ance and departure. 

Ans. Dist. 1065 miles; dep. 939.2 miles W. 

4. Two points are under the same meridian, one in lat¬ 
itude 52° 30' 1ST., the other in latitude 47° 10' N. A ship 
from the southern place sails due east, at the rate of 9 
miles an hour, and two days after meets a sloop that had 
sailed from the other : required the sloop’s direct course, and 
distance run. 

Ans. Course S. 53° 28' E.; dist. 537.6 miles. 

5. If a ship from latitude 48° 27' S., sail S. W. by W 

7 miles an hour, in what time will she reach the parallel 
of 50° south ? Ans. 23.914 hours. 


SECTION III. 

OF TRAVERSE SAILING. 

15. When a ship, in going from one place to anothei, 
sails on different courses, it is called Traverse Sailing. The 
determination of the distance and course, from the place of 
departure to the place of termination, is called compounding 
or working the traverse. This is done by the aid of the 
“ Traverse Table,” which has already been explained, and 
the method of working the traverse, is in all respects simi¬ 
lar to that adopted in the Prob. of Art. 34, page 123. 

EXAMPLES. 

1. A ship from Cape Clear, in lat. 51° 25' 1ST. t sails, 1st, 
S. S. E. i E. 16 miles; 2d, E. S. E. 23 miles; 3d. S. W. 
by W. $ W. 36 miles; 4th, W. f K 12 miles; 5th, S. E. 
by E. \ E. 41 miles : required the distance run, the direct 
course, and the latitude. 



208 


ELEMENTS OF SURVEYING. 


[BOOK V 


AYe first form the table 
below, in which we enter 
the courses, from the table 
of rhumbs, omitting the 
seconds, and then enter 
the latitudes and depart¬ 
ures, taken from the tra¬ 
verse table, to the nearest 
quarter degree. Thus, in 
taking the latitude and 
departure for 25° 18' we 
take for 25^-°. The dif¬ 
ference of latitudes gives 
the line AG, and the dif¬ 
ference of departures the 
line GF. 



TRAVERSE TABLE. 


Courses. 

Dist’s. 

Diff. of Latitude. 

Departure. 

No 


Angle. 


N. 

s. 

E. 

w. 

i 

S. S. E. i E. . . 

25° 18' 

16 


1447 

6.83 


2 

E. S. E. 

67° 30' 

23 


8.80 

21.25 


3 

S. AY. by AY. i AY. 

61° 52' 

36 


17.04 


31.71 

4 

AY. f N. 

81° 33' 

12 

1.77 



11.87 

5 

S. E. by E. i E. . 

59° 03' 

41 


21.12 

35.14 






1.77 

61.43 

63.22 

43.58 






1.77 

43.58 


i 




Diff. 

59.66 

19.64 



Latitude left 51° 25' N. 

Difference of latitude 59.66 miles = 1° 00' S. 


's 


In latitude 50° 25' 1ST. 











































SEO. III.] 


TRAVERSE SAILING. 


209 


Then, by formulas for the solution of right-angled tri 
angles, we have, 


As A 6?, diff. lat. ar. c. 8.224317 
: departure 19.64 1.293141 
: : radius, 10.000000 


As sin course ar. c. 
: radius 

: : departure 19.64 


.504995 

10.000000 

1.293141 


tang course 18° 13' 9.517458 


: distance 


62.83 1.798136 


Therefore the direct course is S. 18° 13' E., and the 
distance 62.83 miles. 


OF PLOTTING. 

16. There is yet another method of finding the direct 
course and distance, much practiced by seamen, although 
it does not afford a high degree of accuracy. It is a 
method by plotting, which requires the use of a mariner’s 
scale and a pair of dividers. 

One of the scales marked on the mariner’s scale, is a 
scale of chords, commonly called a scale of rhumbs, being 
divided to every quarter point of the compass; and there 
is also a second scale of chords divided to degrees. Both 
of these scales are constructed in reference to the same 
common radius, so that the chords on the scale of rhumbs 
correspond to those on the scale of marked chords. The 
manner of using the scales will appear in plotting the last, 
example. 

To construct this traverse, describe a circle with a radius- 
equal to the chord of 60° and draw the meridian NS. 
Then take from the line of rhumbs the chord of the first 
course 2| points, and apply it from S to 1, to the right of 
NS, since the course is southeasterly, and draw A1;.take, 
in like manner, the chord of the second course, 6 points, 
from /S' to 2, and lay it off also to the right of the meri¬ 
dian line. Apply the chord of the third course, 5£ points, 
from S to 3, to the left of the meridian; the fourth course, 
7J- points from N to 4, to the left of NS, this course be¬ 
ing northwesterly and, lastly, apply the chord of the fifth 
course, 5-J points, from S to 5, to the right of NS, and 
join all the lines as in the figure. 

14 







210 ELEMENTS OF SURVEYING. [B>)OK V 

In tlie direction Al t lay off the distance AH= 16 miles 
from a scale of equal parts, and through the extremity R, 
draw RG parallel to A2, and lay off HO — 23 miles. Draw 
CD parallel to A3, and lay off CD = 36 miles; then draw 
DE parallel to A4, and lay off 12 miles; and lastly, draw 
EF parallel to A5, and lay off 41 miles, and F will be the 
place of the ship. Hence, we conclude that AF is the dist¬ 
ance made good, and GAF is the course. 

Applying, then, the distance AF to the scale of equal 
parts, we find it equal to 62f miles; and applying the 
chord Sa to the scale of chords, we find the course GAF 
= 18}°. 

2. A ship sails from a place in latitude 24° 32' N., and 
runs the following courses and distances, viz., 1st, S. W. 
by W. dist. 45 miles ; 2d, E. S. E. dist. 50 miles ; 3d, S. 
W. dist. 30 miles; 4th, S. E. by E. dist. 60 miles; 5th, S. 
W. by S. J W. dist. 63 miles : required her latitude, and 
the direct course and distance from the place left to the 
place arrived at, and the construction of the traverse. 

^ ns j Eat. 22° 3' N., course S. 
t Dist. 149.2 miles. 

3. A ship from lat. 28° 32' N. has run the following 
courses, viz., 1st, N. W. by K 20 miles; 2d, S. W. 40 miles; 
3d, N. E. by E. 60 miles; 4th, S. E. 55 miles ; 5th, W. 
by S. 41 miles; 6th, E. N. E. 66 miles: required her lat¬ 
itude, the distance made good, and the direct course, also 
the construction of the traverse. 

Ans. Dist. 70.2 miles, course E. 

4. A ship from lat. 41° 12' K sails S. W. by W. 21 
miles; S. W. i S. 31 miles ; W. S. W. i S. 16 miles; S. 
| E. 18 miles; S. W. i W. 14 miles; then W. 4 N. 30 
miles: required the latitude, the direct course, and the 
distance. 

Ar>o j^at. 40° 05', course S. 52° 49' W. 

I Dist. 111.7 miles. 

5. A ship runs the following courses, viz.: 

1st, S. E. 40 miles; 2d, N. E. 28 miles; 3d, S W. by 
W. 52 miles; 4th, N W. by W 30 miles; 5th, S. S. E 


PARALLEL SAILING. 


SEC. IV.] 


21! 


36 miles; 6th, S. E. by E. 58 miles: required the direct 
course, and distance made good. 

q /iv j Direct course S. 25° 59' E., or S. S. E. | E., nearly. 

(Distance 95.87 miles. 

6. A ship sails, 1st, N. W. by W. 4 W. 40 miles; 2d 
N. W. by \ N., 41 miles ; 3d, N. by E. 16.1 miles ; and 
4th, N. E. } E. 32.5 miles : required the distance made, 
and the direct course. 

Ans. Course, 21° 54' West of North. Dist. 94.6 miles. 

These examples will, perhaps, suffice to illustrate the 
principles of plane sailing. 

The longitude, made on any course, cannot be deter¬ 
mined by these methods, for this being the arc of the 
equator intercepted between two meridians, cannot be found 
under the supposition that the meridians are parallel. 

The most simple case of finding the difference of lon¬ 
gitude is when the ship sails due east or due west: this is 
called Parallel Sailing. 


SECTION IV. 

PARALLEL SAILING. 

17. The entire theory of parallel sailing is comprehend¬ 
ed in the following proposition, viz.: 

The cosine of the latitude of the ‘parallel , is to radius , as 
the distance run to the difference of longitude. 

Let IQIT represent the equa¬ 
tor, and FJJN any parallel of 
latitude: then, Cl will be the 
radius of the equator, and EF 
the radius of the parallel. 

Suppose FD to be the dis¬ 
tance sailed, then the differ¬ 
ence of longitude will be meas¬ 
ured by IQ , the arc intercept¬ 
ed on the equator. Then, 


P 








212 


ELEMENTS OF SURVEYING. [BOOK V 


since similar arcs are to each 
other as their radii (Geom., 

Bk. Y., Prop, 14), we have, 

EF : Cl : : dist. FD : 
diff. long. IQ. 

But EF is the sine of PF t 
or cosine of FI, the latitude: 
and Cl is the radius of the 
sphere: hence, 

(X)s lat. : R : : distance : 
diff. longitude. 

18. If we denote by D the distance between any two 
meridians, measured on the parallel whose latitude is L ; 
and by D’ the distance between the same meridians meas¬ 
ured on the parallel whose latitude is L ', the arcs are 
similar, and we shall have (Geom., Bk. Y., Prop. 14), 

cos L : D :: cos L’ : D, 
that is, cos L : cos L' : : D : D'. 

Hence, when the longitude made on different parallels is the 
same , the distances sailed are proportional to the cosines of the 
'parallels of latitude. 

19. By referring to Th. Y., Bk. I., we see that in any 
right-angled triangle 

R : cos angle at base :: hyp. : base, 
or cos E : R : : EC : EG; 
and by comparing this with the propor¬ 
tion, 

cos lat. : R : : dist. : diff. long; 
we see, that if in a right-angled triangle 
the angle at the base be made equal to 
the latitude of the parallel, and the base 
to the distance run ; then, the hypothenuse will represent 
the difference of longitude. 

It follows therefore, that any problem in parallel sail 
ing, may be solved as a simple case of plane sailing. For, 
if we regard the latitude as the course, the distance run 
as the base, the difference of longitude will be the hypo 
thenuse of the corresponding right-angled triangle. 



P 










SEC. IV.] 


PARALLEL SAILING. 


213 


EXAMPLES. 

1. A ship from latitude 53° 56 N., longitude 10° 18' 
E., has sailed due west, 236 miles : required her present 
longitude. 

By the rule 

As cos lat. 53° 56' . ar. c. . .230087 

: radius. 10.000000 

: : distance 236 . 2.372912 

. 2.602999 

10° 18* E. 

: 6° 40' W. 

3° 38' E. 


2. If a ship sails E. 126 miles from the North Cape, 
in lat. 71° 10' N., and then due N., till she reaches lat. 
73° 26' 1ST.; how far must she sail W. to reach the meri¬ 
dian of the North Cape? 

Here the ship sails on two parallels of latitude, first cm 
the parallel of 71° 10', and then on the parallel of 73° 26', 
and makes the same difference of longitude on each parallel 

Hence, by Art. 18, 


As cos lat. 71° 10' 

arith. comp. 0.491044 

: distance 

126 

. 2.100371 

: : cos lat. 

73° 26 

. 9.455044 

: distance 

111.3 

. 2.046459 


diff. long. 400.8 


Long, left 
Diff. long. = 


400 , 
60 


Long. 


3. A ship in latitude 32° N. sails due E. till her dif¬ 

ference of longitude is 384 miles: required the distance 
run. Ans. 325.6 miles. 

4. If two ships in latitude 44° 30' N., distant from 
each other 216 miles, should both sail directly S. till their 
distance is 256 miles, what latitude would they arrive at? 

Ans. 32° 17' N, 









214 


NAVIGATION 


BOOK V 


5. Two ships in the parallel of 47° 54 1ST., have 9° 35' 
difference of longitude, and they both sail directly S., a 
distance cf 836 miles: required their distance from each 
other at the parallel left, and at that reached. 

Ans. 385.5 miles, and 479.9 miles 


SECTION V. 

MIDDLE LATITUDE SAILING. 

20. Having seen how the longitude which a ship makes 
when sailing on a parallel of latitude may be determined, 
we come now to examine the more general problem, viz., 
to find the longitude which a ship makes when sailing 
upon any oblique rhumb. 

There are two methods of solving this problem, the one 
by what is called middle latitude sailing , and the other by 
Mercator’s sailing. The first of these methods is confined 
in its application, and is moreover somewhat inaccurate 
even where applicable; the second is perfectly general, and 
rigorously true; but still there are cases in which it is advi¬ 
sable to employ the method of middle latitude sailing, in 
preference to that of Mercator’s sailing. It is, therefore, 
proper that middle latitude sailing should be explained, 
especially since, by means of a correction to be hereafter 
noticed, the usual inaccuracy of this method may be 
rectified. 

Middle latitude sail¬ 
ing proceeds on the 
s upposition that the de- 
parture or sum of all 
the meridional distan¬ 
ces, b'b , cc, d!d ) &c., 
from 0 to T, is equal 
to the distance M'M 
between the meridians 
passing through 0 and r l\ measured on the parallel of lati¬ 
tude equally distant from 0 and T. 











SEC. V.- 


MIDDLE LATITUDE SAILING. 


215 


The middle latitude is half the sum of the two extreme 
latitudes, if they are both of the same name, and half 
their difference, if they are of contrary names. 

The supposition above becomes very inaccurate when the 
course is small, and the distance run great; for it is plain that 
the middle latitude distance will receive a much greater acces¬ 
sion than the departure, if the track OT cuts the successive 
meridians at a very small angle. 

The principal approaches nearer to accuracy as the angle 
0 of the course increases, because then as but little ad¬ 
vance is made in latitude, the several component depart¬ 
ures lie more in the immediate vicinity of the parallel M'M. 
But still, in very high latitudes, a small advance in lat¬ 
itude makes a considerable difference in meridional dist¬ 
ance ; hence, this principle is not to be used in such lat¬ 
itudes, if much accuracy is required. 

By means, however, of a small table of corrections, con 
structed by Mr. Workman , the imperfections of the middle 
latitude method may be removed, and the results of it ren¬ 
dered in all cases accurate. This table we have given at 
the end of this work. 

21. The rules for middle latitude sailing may be thus 
deduced. 

We have seen, in the first case of plane 
sailing, that if a ship sails on an oblique 
rhumb from 0 to T\ that the hypotlienuse 
OT will represent the distance; OT' the 
difference of latitude, and T'T, the depart¬ 
ure. Now, by the present hypothesis, 
the departure T T is equal to the middle 
parallel of latitude between the meridians 
of the places sailed from and arrived at: 

30 that the difference of longitude of these two places is the 
same as if the ship had sailed the distance T'T on the mid¬ 
dle parallel of latitude. The determination of the differ¬ 
ence of longitude is, therefore, reduced to the case of par¬ 
allel sailing: for, T'T now representing the distance on the 
parallel, if the angle T TO' be made equal to the latitude of 





216 


NAVI NATION. 


[BOOK V. 


that parallel, we shall have, by the last case, the difference 
of longitude represented by the hypothenuse O T. We 
therefore have the following theorems: 

I. In the triangle O'TT', 

cos O'TT' : TT' : : R : TO '; 

that is, 

cos mid. lat. : departure : : R : diff. longitude. 

II. In the triangle O'TO 

sin O' : OT : : sin 0 : 0'T\ 

that is, since sin O' = cos O'TT' 

cos mid. lat. : distance :: sin. course : diff. longitude. 

III. In the triangle OTT' f we have 

R : tangent 0 : : OT' : TT '; 

comparing this with the first proportion, and observing 
that the extremes of this are the means of that, we have 

OT' : O'T :: cos O'TT' : tang 0; 

that is, 

diff. lat. : diff. long. : : cos mid. lat. : tang course. 

These three propositions comprise the theory of mid 
die latitude sailing; and when to the middle latitude sail 
ing, the proper correction, taken from Mr. Workman’s table, 
is applied, these theorems will be rendered accurate. 

In the table of pages 93 and 94, the middle latitude is 
to be found in the first column to the left. Then, along 
the horizontal line, and under the given difference of lat¬ 
itude, is inserted the proper correction to be added to the 
middle latitude to obtain the latitude in which the meri¬ 
dian distance is accurately equal to the departure. Thus, 
if the middle latitude be 37°, and the difference of latitude 
18°, the correction will be found on page 94, and is equal 
to 0° 40'. 


EXAMPLES. 

1 . A ship, in latitude 51° 18' 1ST., longitude 22° 6' W., 
is bound to a place in the S E. quarter, 1024 miles dis¬ 
tant, and in lat. 37° 1ST.: what is her direct course and dis- 


SEC. V.] MIDDLE LATITUDE SAILING. 


217 


lance, as also the difference of longitude between the two 
places ? 

Lat. from 51° 18' 1ST. ) . 

Lat. to 37° 0 N. S Sum of latltu(?es • • 88 ° 18 ' 

- Mid. lat.44° 9' 

Diff. lat. 14° 18 = 858 miles. 


As distance 1024 
: radius 

: : diff. lat. 858 


6.989700 

10.000000 

2.933487 


. cos course 83° 5' 9.923187 


Cos mid lat 44° 9'ar c 0.144167 
: tang course 33° 5 9.813899 
: : diff. lat. 858 2.933487 


: diff. long. 779 2.891553 


In this operation the middle latitude has not been cor¬ 
rected, so that the difference of longitude here determined 
is not without error. To find the proper correction, look 
for the given middle latitude, viz., 44° 9', in the table of 
corrections, the nearest to which we find to be 45° ; against 
this and under 14° diff. of lat. we find 27'; and also, under 
15° we find 3T, the difference between the two being 4'; 
hence, corresponding to 14° 18' the correction will be about 
28'. Hence, the corrected middle latitude is 44° 87' r 
therefore, 

Cos corrected mid. lat. 44° 87' ar. comp. 0.147629 
: tang, course 83° 5' . . 9.813899 

: : diff. lat. 858 . . . 2.933487 


: diff. long 785.3 


2.895015 


therefore, the error in the former result is about 6£ miles. 

2. A ship sails in the N. W. quarter, 248 miles, till her 
departure is 135 miles, and her difference of longitude 310 
miles : required her course, the latitude left, and the lat¬ 
itude come to. 


. ) Course N. 82° 59 W .; 

US, i Lat. left 62° 27' N .; lat. in 65° 55' N. 

3 . A ship, from latitude 87° 1ST., longitude 9° 2' W ,., 
paving sailed between the N. and W., 1027 miles, reckons 
that she has made 564 miles of departure : what was her 
direct course, and the latitude and longitude reached? 

. j Course JST. 33° 19' W., or N. W. rearly; 
nS ' I Lat. 51° 13 N.; long. 22° 8' W. 










218 


NAVIGATION 


[BOOK V 


4. Required the course and distance from the east point 
of St. Michael’s, lat. 37° 48' N., long. 25° 13' AM., to the 
Start Point, lat. 50° 13' 1ST., long. 3° 38' AY. ; the middle 
latitude being corrected by AYorkman’s table. 

Ans . Course N. 51° 11' E.; dist. 1189 miles. 


Mercator’s sailing. 


22. It has already been observed, that when a ship 
sails on an oblique rhumb, the departure, the difference of 
latitude, and the distance run, are truly represented by 
the sides of a right-angled triangle. 

Thus, if a ship sails from A to B, the 
departure B'B will represent the sum of 
all the very small meridian distances, 
or elementary departures, b'b, p"p, &c.; 
the difference of latitude AB' will re¬ 
present, in like manner, the small dif¬ 
ferences of latitude Ah', b'p', &c.; and 
the hypothenuse AB, will express the 
sum of the distances corresponding to 
these several differences of latitude 
and departure. Each of these elements is supposed to be 
taken so small, as to form on the surface of the sphere a 
series of triangles, differing insensibly from plane triangles. 

Let ABB' be a triangle, in which the angle A repre¬ 
sents the course, AB' the difference of latitude, B'B the 
departure, and AB the distance run. Produce the side 
AB' to C, until CC' shall be equal to the difference of 
longitude of the two extremities of the course : then, for 
the sake of distinction, we call 



AB' = the proper difference of latitude, 

A O' = the meridional difference of latitude, 
and we are now to explain the manner of constructing a 
table, called a table of meridional parts, which will furnish 
the meridional differences of latitude when the proper differ¬ 
ences are known. 

Let Ab'b represent one of the elementary triangles; b'b 
will then be one of the elements of departure; and Ah' 
the corresponding difference of latitude. Now, as b'b is a 
small arc of a parallel of latitude, it is to a portion of the 








SEO. V.] 


MERCATOR’S SAILING 


219 


equator containing an equal number of degrees, as tlie co¬ 
sine of its latitude is to radius (Art. 17). This similar 
portion of the equator, is the difference of longitude be¬ 
tween b' and b. 

Suppose, now, that Ab' is prolonged to p\ making p'p 
equal to the difference of longitude between b and b' : then 

bb' : pp' : : cos lat. b'b : R (Art. 17.) 

But, by similar triangles, we have 

bb' : pp' : : Ab' : Ap', 
and consequently, 

proper lat. Ab' : mer. diff. of lat. Ap' : : cos lat. bb' : 1 . 

Denoting the proper difference of latitude by d , the 
meridional difference of latitude by D, the latitude of b'b 
by Z, and the radius by 1, which is, indeed, the radius of 
the table of natural sines, we shall have 

d : D :: cos l : 1, 

which gives 

D = d secant l, since - ^ 7 = sec. 1. 

cos l 

If then, we know the latitude l of the beginning of a 
course, and the proper difference of latitude d of the ex¬ 
tremity of the course, we can easily find the meridional 
latitude D corresponding to that course. 

The determination of AC which represents the meri¬ 
dional difference of latitude, involves the determination Oi 
all the elementary parts, on which it depends. If d be 
taken equal to 1', we shall have from the equation above 
D= V sec. I , or D = sec. 

it being understood that l expresses minutes or geographi¬ 
cal miles. 

From this equation, the value of R, corresponding to 
every minute of Z, from the equator to the pole, may be 
calculated; and from the continued addition of these, there 
may be obtained, in succession, the meridional parts cor¬ 
responding to 1', 2', 3', 4', &c., of proper latitude, and when 
registered in a table, they form a table of meridional parts, 
given in all books on Navigation. 

The following may serve as a specimen of the manner 
in which such a table may be constructed, and, indeed, of 
the manner in which the first table of meridional parts was 



I 


\ 


220 NAVIGATION. [BOOK V 

actually formed by Mr. Wright, the proposer of this valu¬ 
able method. 

Mer. pts. of 1' - nat. sec. 1'. 

Mer. pts. of 2' = nat. sec. 1' + nat. sec. 2'. 

Mcr. pts. of 3' = nat. sec. 1 + nat. sec. 2 4- nat. sec. 3'. 

Mer. pts. of 4' = nat. sec. 1' + nat. sec. 2' 4- nat. sec. 3' 4- &c 

Hence, by means of a table of natural secants we have 

Nat. Secs. Mer. Pts. 

Mer. pts. of V = 1.000000 = 1.0000000 

Mer. pts. of 2' = 1.0000000 + 1.0000000 = 2.0000002 
Mer. pts. of 3' = 2.0000002 + 1.0000004 = 3.0000006 
Mer. pts. of 4' = 3.0000006 4- 1.0000007 = 4.0000013, &c. 
There are other methods of construction, but this is the 
most simple and obvious. The meridional parts thus de¬ 
termined, are all expressed in geographical miles, because 
in the general expression 

D — 1' sec. Z, 

1 ' is a geographical mile. 

23. Having thus formed the table of meridional parte, 
if we find from it, the meridional parts corresponding to 
the latitudes of the place left and the place arrived at, 
their difference will be the meridional difference of lat¬ 
itude, or the line AC in the diagram. The difference of 
longitude denoted by C'C may then be found by the fol¬ 
lowing proportion. 

I. As radius is to the tangent of the course , so is the meri¬ 
dional difference of latitude to the difference of longitude . 

But if the departure be given instead of the course, then, 

II. As the proper difference of latitude is to the departure , 
so is the meridional difference of latitude to the longitude. 

Other proportions may also be deduced from the diagram. 

EXAMPLES. 

As an example of Mercator’s or rather Wright’s, sailing, 
let us take the following: 

1. Required the course and distance from the east point 
of St. Michael’s to the Start point: the latitudes being 37° 
48 H., and 50° 13' N., and the longitudes 25° 13' W, and 
3° 38' W. 


8EC. V.] 


MERCATOR’S CHART. 


221 


Start Point, lat. 50° 13' N. 
St. Michael’s, lat. 37° 48' N. 

Proper difference of lat. 12° 25' 

60 

Diff. in miles 745 


Mer. pts. 3495 
Mer. pts. 2453 

Mer. diff. 1042 

Diff. of long. 21° 35' 

60 


Diff. in miles 1295 


Now, let us suppose that we have 
sailed from A to B: we shall then 
know AB' equal proper diff. lat. = 745 
miles; A O' — meridional diff. of lat. = 
1042; and O' 0 = the difference of lon¬ 
gitude equal to 1295 miles. It is re¬ 
quired to find the course B'AB 1 and the 
distance AB. 



As AO' 
: radius 
:: O'O 


For the Course. 


For the Distance. 


1042 

1295 


6.982132 

10.000000 

3.112270 


As cos A 51° 11' 
: AB' 745 
: : radius 


0.202850 

2.872156 

10.000000 


tang. A 51° 11' E. 10.094402 


AB 1189 


3.075006 


2. A ship sails from latitude 37° N. longitude 22° 56' 
\V\, on the course N. 33° 19' E.: till she arrives at 51° 
18' N.: required the distance sailed, and the longitude ar¬ 
rived at. Ans. Dis. 1027 miles; long. 9° 45' W 


mercator’s chart. 

24. Mercator’s Chart is a Map constructed for the use 
of Navigators. In this chart all the meridians are repre¬ 
sented by straight lines drawn parallel to each other, and 
the parallels of latitude are also represented by parallel 
straight lines drawn at right-angles to the meridians. 

The chart may be thus constructed. Draw on the lower 
part of the paper a horizontal line to represent the parallel 
of latitude which is to bound the southern portion of the 
chart. From a scale of equal parts, corresponding in size 


















222 


NAVIGATION. 


[BOOK V 


to tlie extent of the map to be made, lay off, on this line, 
any number of equal distances, and through the points 
draw a series of parallels to represent the meridians. 

Then draw a line on the side of the map, and for the 
second parallel of latitude, find from the table of meri¬ 
dional parts the meridional difference of latitude corres¬ 
ponding to the degrees between the first and second par¬ 
allel, and lay off this distance for the interval between the 
two parallels. Then find the meridional difference between 
the second and third, and lay it off in the same way for 
the third parallel, and so on, for the fourth, fifth, &c. 

A place whose latitude and longitude are known, may 
be laid down in the same manner; for it will always be 
determined by the intersection of the meridian and parallel 
of latitude. 

If the chart is constructed on a small scale, the divisions 
on the graduated lines, may be degrees: instead of minutes; 
and the meridians and parallels may be drawn only foi 
every fifth or tenth degree. 

We have already seen (Art. 23), that the meridional 
difference of latitude bears a constant ratio to the difference 
of longitude, so long as the course remains unchanged: 
and hence we see that on Mercator’s chart, every rhumb 
will be represented by a straight line. 

LINE OF MERIDIONAL PARTS ON GUNTER’S SCALE. 

25. This scale corresponds exactly with the table of me¬ 
ridional parts / excepting, that in the table, the circle is divid 
ed to minutes, while the scale is divided only to degrees. 
A scale of equal parts is placed directly beneath the scale 
of meridional parts; if the former corresponds to divisions 
of longitude, the latter will represent those of latitude. 
Hence, a chart may be constructed from those scales, by 
using the scale of equal parts for the lines of longitude, 
and the scale of meridional parts for those of latitude. 


A TABLE 


OF 

LOGARITHMS OF NUMBERS 

FROM 1 TO 10,000. 


N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

i 

D-OOOOOO 

26 

1 -414973 

5i 

1 -707670 

76 

1 -880814 

2 

o-3oio3o 

27 

1 -43i364 

52 

1-716003 

77 

1 -886491 

3 

0-477121 

28 

1 -447i58 

53 

1-724276 

78 

1-892095 

4 

0-602060 

29 

1 -462398 

54 

1-732394 

79 

1-897627 

5 

0-698970 

3o 

1 *477 121 

55 

1 -74o363 

80 

1-908090 

6 

0-778151 

3i 

1 -49i362 

56 

] -748188 

81 

1 -908486 

7 

0-845098 

32 

1-5o5i5o 

5 i 

1 -755875 

82 

1-913814 

8 

0-903090 

33 

1 -5i85i4 

58 

1 -763428 

83 

1 -919078 

9 

0-954243 

34 

1 -531479 

5 9 

1 -770862 

84 

1-924279 

IO 

I-OOOOOO 

35 

1• 544068 

60 

1 - 77815 x 

85 

1-929419 

11 

1-041393 

36 

1 -5563o3 

61 

1 -78533o 

86 

1 -934498 

12 

1-079181 

37 

1 -568202 

62 

1-792392 

87 

1-939619 

i3 

1 -113943 

38 

1-579784 

63 

1-799341 

88 

1-944483 

14 

1•146128 

3 9 

1-591065 

64 

1-806181 

89 

1-949390 

i5 

1-176091 

40 

1-602060 

65 

1-812913 

90 

1-954243 

16 

1-204120 

4i 

1-612784 

66 

1-819544 

9i 

1-959041 

H 

1•230449 

42 

1-628249 

67 

1-826075 

92 

1-963788 

18 

1•255273 

43 

1-633468 

68 

1-8325o9 

93 

1-968483 

19 

1•278764 

44 

1-643453 

69 

1-838849 

94 

1-973128 

20 

1-3oio3o 

45 

1•653213 

70 

1-845098 

9 5 

1-977724 

21 

1-322219 

46 

1-66275s 

7i 

i-85i258 

96 

1 -982271 

22 

1-342423 

47 

1-672098 

72 

1-857333 

97 

1-986772 

23 

1-361728 

48 

1-681241 

73 

1-863323 

98 

1-991226 

24 

1-38o2ii 

49 

1•690196 

74 

1•869232 

99 

1-996636 

2D 

1-397940 

5o 

1-698970 

75 

1•876061 

100 

2•OOOOOO 


Remark. In the following table, in the nine right hand 
columns of each page, where the first or leading figures 
change from 9’s to 0’s, points or dots are introduced in 
stead of the 0’s, to catch the eye, and to indicate that from 
thence the two figures of the Logarithm to be takeu from 
the second column, stand in the next line below 







































2 A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 


N. 

0 

1 

2 

3 

A 

5 

6 

7 

8 

9 

D. 

IOO 

000000 

0434 

0868 

i 3 oi 

1734 

2166 

2598 

3029 

3461 

3891 

432 

IOI 

4321 

4761 

5 181 

5609 

6 o 38 

6466 

6894 

7 321 

7748 

8174 

428 

102 

8600 

9026 

9 45 i 

9876 

• 3 o 0 

•724 

1147 

1 5 7 o 

1993 

241 5 

424 

io 3 

012837 

325 9 

368 o 

4100 

4521 

4 9 4 o 

536 o 

5779 

6197 

6616 

419 

104 

7 o 33 

745 1 

7868 

8284 

8700 

on6 

9 53 2 

9947 

• 36 1 

•775 

416 

io 5 

021189 

i 6 o 3 

2016 

2428 

2841 

0252 

3664 

407 D 

4486 

4896 

412 

106 

53 o 6 

5715 

6 i 25 

6533 

6942 

735 o 

7 7 5 7 

8164 

85 7 1 

8978 

408 

107 

9384 

0789 

•i 9 5 

•600 

1004 

1408 

1812 

22l6 

2619 

3 o 2 I 

4 o 4 

108 

o33424 

3826 

4227 

4628 

5029 

543 o 

583 o 

623 o 

6629 

7028 

400 

109 

7426 

7825 

8223 

8620 

9017 

9414 

9811 

•207 

•602 

•998 

3 9 6 

110 

041 3 9 3 

1787 

2182 

2576 

2969 

3362 

3 7 55 

4148 

4540 

4 q 3 2 

3 9 3 

111 

5323 

5714 

6 io 5 

64 9 5 

6885 

7275 

7664 

8 o 53 

8442 

883 o 

38 9 

112 

9218 

9606 

999 3 

•3 80 

•766 

11 53 

1 538 

1924 

2309 

2694 

386 

11 3 

050078 

3463 

3846 

423 o 

46 i 3 

4996 

5378 

5760 

6142 

6524 

382 

114 

6 9 o 5 

7286 

7666 

8046 

8426 

88 o 5 

9185 

9 563 

0942 

•320 

379 

I ID 

060698 

1075 

1452 

1829 

2206 

2582 

2 9 58 

3333 

3709 

4 o 83 

376 

I 16 

4458 

4832 

5206 

558 o 

5 9 53 

6326 

6699 

7071 

7443 

7 8 i 5 

372 

1*7 

8186 

8557 

8928 

9298 

9668 

••38 

•407 

•776 

1 i 45 

i 5 i 4 

369 

118 

071882 

2250 

2617 

2 9 85 

3352 

3718 

4 o 85 

445 1 

4816 

5 i 82 

366 

u 9 

5547 

5 9 I 2 

6276 

6640 

7004 

7368 

773 1 

8094 

8457 

8819 

363 

120 

079181 

Q 543 

9904 

•266 

•626 

•987 

1 347 

1707 

2067 

2426 

36 o 

121 

082785 

3144 

3 do 3 

386 i 

4219 

4576 

4934 

5291 

5647 

6004 

35 7 

122 

636 o 

6716 

7071 

7426 

7781 

81 36 

8490 

8845 

9 * 9 8 

9552 

355 

123 

9905 

•258 

•611 

•963 

1 3 1 5 

1667 

2018 

23 7 o 

2721 

0071 

35 i 

124 

098422 

3772 

4122 

4471 

4820 

5 169 

55 i 8 

5866 

621 5 

656 ? 

349 

125 

6910 

7267 

7604 

79 5 i 

8298 

8644 

8990 

9335 

9681 

••26 

346 

126 

100871 

0715 

1069 

i 4 o 3 

1747 

2091 

2434 

2777 

3119 

3462 

343 

127 

38 o 4 

4146 

4487 

4828 

5 i 6 9 

55 io 

585 1 

6191 

653 1 

6871 

34 o 

128 

7210 

7549 

7888 

8227 

8565 

8 9 o 3 

9241 

9 5 79 

9916 

•253 

338 

129 

110890 

0926 

1263 

*599 

1934 

2270 

26o5 

2940 

3275 

3609 

335 

i 3 o 

1i 3 9 43 

4277 

4611 

4944 

5278 

56 i 1 

5943 

6276 

6608 

6940 

333 

1 3 1 

7271 

7608 

7934 

8265 

85 9 5 

8926 

9256 

9586 

991 5 

•245 

33 o 

132 

i2o5->4 

0903 

I 231 

i 56 o 

1888 

2216 

2544 

2871 

0198 

3525 

328 

1 33 

3852 

4178 

45 o 4 

483 o 

5 1 56 

5481 

58 o 6 

6 i 3 i 

6406 

6781 

325 

1 34 

7105 

7429 

7753 

8076 

8399 

8722 

9045 

9368 

9690 

••12 

323 

1 35 

i 3 o 334 

o 655 

0977 

1298 

1619 

1939 

2260 

258 o 

2900 

3219 

321 

1 36 

3539 

3858 

4177 

4496 

4814 

5 1 33 

545 1 

5769 

6086 

64 o 3 

3 18 

i 37 

6721 

7037 

7354 

767 1 

7987 

83 o 3 

8618 

8934 

9249 

9564 

3 1 5 

1 38 

9879 

•194 

• 5 o 8 

•822 

11 36 

i 45 o 

1763 

2076 

2389 

2702 

314 

1 3 9 

i 43 oi 5 

3327 

363 9 

3 9 5 i 

4263 

4574 

4885 

5 196 

55 o 7 

58 i 8 

3 11 

140 

146128 

6438 

6748 

7 o 58 

7367 

7676 

7985 

8294 

86 o 3 

8911 

309 

141 

9 2I 9 

9D27 

9835 

•142 

•449 

• 7 56 

io 63 

i 3 7 o 

1676 

1982 

307 

142 

152288 

25 g 4 

2900 

32 o 5 

3 dio 

38 1 5 

4120 

4424 

4728 

5 o 32 

3 o 5 

143 

5336 

6640 

5 9 43 

6246 

6549 

6852 

7154 

7457 

7759 

8061 

3 o 3 

144 

8362 

8664 

8 9 65 

9266 

9567 

9868 

•168 

•469 

•769 

1068 

3 oi 

145 

161 368 

1667 

1967 

2266 

2564 

2863 

3 161 

3460 

3 7 58 

4 o 55 

299 

146 

4353 

465 o 

4947 

5244 

554 i 

5838 

61 34 

643 o 

6726 

7022 

297' 

147 

7317 

7613 

7008 

82 o 3 

8497 

8792 

9086 

9380 

9674 

9968 

295 

148 

170262 

o 555 

0848 

1141 

1434 

1726 

2019 

231 I 

26 o 3 

2895 

293 

149 

3 186 

3478 

3769 

4060 

435 i 

4641 

4 9 32 

5222 

55 12 

5802 

291 

i 5 o 

176091 

638 i 

6670 

6969 

7248 

7536 

7825 

811 3 

8401 

8689 

289 

1 5 1 

8077 

9264 

9 552 

9 § 3 9 

•126 

•413 

•699 

• 9 85 

1272 

1 558 

287 

1 5 a 

181844 

2129 

2415 

2700 

2985 

3270 

3555 

383 9 

4123 

4407 

285 

1 53 

4691 


52D9 

5542 

58 2 5 

6108 

6391 

6674 

6956 

7239 

283 

1 54 

7521 

7803 

8084 

8366 

8647 

8928 

9209 

9490 

977 i 

•• 5 1 

281 

1 55 

i 9 o 332 

0612 

0892 

1171 

1 45 1 

1730 

2010 

2289 

2667 

2846 

279 

1 56 

3 1 25 

34 o 3 

368 i 

3969 

4287 

45 r 4 

4792 

5 o 6 9 

5346 

5623 

278 

157 

5899 

6176 

6453 

6729 

7005 

7281 

7 5 d 6 

7 832 

8107 

8382 

276 

1 58 

8607 

8 9 32 

9206 

9481 

9755 

••29 

• 3 o 3 

•577 

• 85 o 

1124 

274 

1 5 9 

201397 

1670 

1943 

2216 

2488 

2761 

3 o 33 

33 o 5 

35 77 

3848 

272 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 






























































8 


A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

0 

1 


3 

4 

5 

6 

7 

8 

9 

D. 

160 

204120 

4391 

4663 

4934 

5204 

5475 

5746 

6016 

6286 

6556 

271 

l6l 

6826 

7096 

7365 

7634 

7904 

8173 

8441 

8710 

8979 

9247 

269 

162 

9515 

9783 

••5i 

•319 

•586 

•853 

1121 

1 388 

1654 

1921 

267 

1 63 

2 E 2188 

2454 

2720 

2986 

3252 

35i8 

3783 

4049 

43 1 4 

4579 

266 

164 

4844 

5109 

53 7 3 

5638 

5902 

6166 

6430 

6694 

6957 

7221 

264 

1 65 

7484 

7747 

8010 

8273 

8536 

8798 

9060 

9 323 

9 o85 

9846 

262 

166 

2 JO 108 

0370 

q 63 i 

0892 

1 153 

1414 

1675 

io36 

2196 

2456 

261 

167 

2716 

2976 

3236 

3496 

3 7 55 

4oi5 

4274 

4033 

4792 

5o5i 

25g 

168 

5 3 39 

5568 

5826 

6084 

6342 

6600 

6858 

7115 

7372 

n 763 o 

258 

169 

7887 

8144 

8400 

8657 

8918 

9170 

9426 

9682 

9938 

•193 

206 

170 

33044$ 

0704 

0960 

1215 

1470 

1724 

1979 

2 234 

2488 

2742 

254 

1 7 1 

2996 

325 g 

3 004 

3757 

4011 

4264 

4517 

4770 

5o23 

5276 

253 

172 

5528 

5781 

6o33 

6285 

6537 

6789 

7041 

7292 

7544 

779 5 

252 

173 

8046 

8297 

8548 

8799 

9049 

9299 

955o 

9800 

*®5o 

•3oo 

25o 

174 

240549 

0799 

1048 

1207 

i 546 

1 79 5 

2044 

2293 

2541 

2790 

249 

173 

3o38 

3286 

3534 

3782 

4o3o 

4277 

4525 

4772 

5019 

6266 

248 

176 

5513 

5759 

6006 

6252 

6499 

6745 

6991 

7237 

7482 

7728 

246 

177 

.7973 

8219 

8464 

8709 

8934 

9198 

9443 

9687 

9932 

•176 

245 

178 

200420 

0664 

qqo8 

11 5 1 

1395 

i638 

1881 

2125 

2368 

2610 

243 

179 

2853 

3096 

3338 

358o 

3822 

4064 

43 o 6 

4548 

4790 

5o3i 

242 

180 

255273 

5514. 

5 7 55 

5996 

623] 

6477 

6718 

6o58 

7198 

7439 

241 

181 

7679 

79 l8 

8158 

83o8 

8637 

8877 

9116 

9355 

9694 

9833 

239 

182 

260071 

q 3 io 

o548 

0787 

1025 

1263 

i 5 oi 

1739 

1076 

2214 

238 

1 83 

2451 

2688 

2920 

3 i 62 

3399 

3636 

3873 

4109 

4346 

4582 

237 

184 

4818 

5 o 54 

5290 

5525 

5761 

6996 

6232 

6467 

6702 

6937 

235 

1 85 

7172 

7406 

7641 

7875 

8110 

8344 

8578 

8812 

9046 

9279 

234 

186 

9613 

9746 

9980 

•213 

•446 

•679 

•912 

1144 

1377 

1609 

233 

187 

271842 

2074 

23 o 6 

2538 

2770 

3ooi 

3233 

3464 

3696 

3927 

232 

188 

415-8 

4389 

4620 

485o 

5o8i 

53 11 

5542 

5772 

6002 

6232 

23 o 

189 

6462 

6692 

6921 

715 i 

7380 

7609 

7 838 

8067 

8296 

8525 

229 

1 90 

278754 

8982 

9211 

943 q 

9667 

9895 

•123 

•35 1 

•5 7 8 

•806 

228 

191 

28 io 33 

1261 

1488 

170 

1942 

2169 

23g6 

2622 

2849 

3 oj 5 

227 

192 

33oi 

3527 

8753 

8979 

42 o 5 

443 1 

4606 

4882 

5107 

5332 

226 

193 

5557 

5782 

6007 

6232 

6456 

6681 

6905 

7i3o 

7354 

7 5 7 8 

225 

194 

7802 

8026 

8249 

8473 

8696 

8920 

9143 

9366 

9089 

9812 

223 

195 

290035 

0257 

0480 

0702 

0926 

1 147 

1369 

i5gi 

1 813 

2 o 34 

222 

196 

2256 

2478 

2699 

2920 

3141 

3363 

3584 

38o4 

4025 

4246 

221 

197 

4466 

4687 

4907 

5127 

5347 

5567 

5787 

6007 

6226 

6446 

220 

198 

6665 

6884 

7104 

7323 

7542 

7761 

7979 

8198 

8416 

8635 

219 

*99 

8853 

9071 

9289 

9507 

9725 

9943 

•161 

•378 

•5 9 5 

•813 

218 

2 CO 

3oio3o 

1247 

1464 

1681 

1898 

2114 

233 1 

2547 

2764 

2980 

2I 7 

201 

3196 

3412 

3628 

3844 

4059 

4275 

4491 

4706 

4921 

5i36 

2l6 

202 

5351 

5566 

5781 

5996 

6211 

6425 

663 9 

6854 

7068 

7282 

2 I 5 

203 

7496 

7710 

7924 

8187 

835 1 

8564 

8778 

8991 

9204 

9417 

2 1 3 j 

204 

9630 

9843 

**56 

•268 

•481 

•693 

•906 

1118 

i33o 

1542 

212 1 

205 

311754 

1966 

2I 77 

2889 

2600 

2812 

3o23 

3234 

3445 

3656 

21 I i 

206 

3867 

4078 

4289 

4499 

4710 

4920 

5i3o 

5340 

555i 

5760 

210 J 

207 

5970 

6180 

63 9 o 

6699 

6809 

7018 

7227 

7436 

7646 

7864 

2091 

208 

8o63 

8272 

8481 

8689 

8898 

9106 

93 i 4 

9522 

9730 

9938 

208 [ 

209 

320146 

o354 

o 562 1 

1 

0769 

°977 

1184 

1391 

1598 

i8o5 

2012 

207 

210 

322219 

2426 

2633 

2839 

3o46 

3252 

3458 

3665 

3871 

4077 

506 

211 

4282 

4488 

4694 

4899 

5io5 

5310 

55 1 6 

5721 

5926 

6 1 3 1 

:o5 

212 

6336 

654 i 

6745 

6900 

7i55 

7 35 9 

7563 

7767 

7972 

8176 

204 

2 l 3 

838o 

8583 

8787 

8991 

9194 

9398 

9601 

9 8o5 

®®*8 

•211 

203 

214 

33 o 4 i 4 

0617 

0819 

1022 

1225 

1427 

i63o 

183 2 

2 o 34 

2 236 

202 

2 15 

2438 

2640 

2842 

3 044 

3246 

3447 

3649 

385o 

4 o 5 i 

4253 

202 

216 

4454 

4655 

4856 

5 o 57 

5257 

5458 

5658 

5859 

6059 

6260 

201 

217 

6460 

6660 

6860 

7060 

7260 

7459 

7 65 9 

7858 

8o58 

8257 

200 

218 

8456 

8656 

8855 

9054 

9253 

945 1 

9650 

9849 

•°47 

•246^ 

1 99 

219 

34 o 444 

0642 

0841 

1039 

1237 

1435 

i 632 

i83o 

202$ 

2225 

198 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 1 

9 

D. 











- 

—J 


15 











































































i A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


p- 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

I 

i 220 

342423 

2620 

2817 

3oi4 

3212 

3409 

36o6 

38o2 

3999 

4196 

197 

[ 221 

4392 

4589 

4 7 85 

4981 

5i 78 

53 7 4 

55 7 o 

5 7 66 

5962 

6107 

196 

! 222 

6333 

6549 

6744 

6q3q 

7135 

7 33o 

7 525 

7720 

7 9 i5 

8110 

196 

223 

83o5 

85oo 

8694 

8889 

9083 

9278 

9472 

9666 

9860 

••54 

194 

224 

350248 

0442 

o636 

0829 

1023 

1216 

1410 

i6o3 

1796 

1989 

193 

225 

2i83 

23 7 5 

2568 

2761 

2954 

3147 

3339 

3532 

3724 

8916 

193 

226 

4108 

43oi 

4493 

4685 

4876 

5o68 

5260 

5452 

5643 

5834 

192 

227 

6026 

6217 

6408 

6599 

6790 

6981 

7172 

7 363 

7 554 

7744 

191 

228 

7935 

8i25 

83 1 6 

85o6 

8696 

8886 

9076 

9266 

9456 

9646 

190 

229 

9o35 

**25 

*2l5 

•404 

•5 9 3 

• 7 S3 

•972 

ii6i 

i35o 

i539 

189 

23o 

361728 

1917 

2105 

2294 

2482 

2671 

2869 

3o48 

3236 

3424 

188 

231 

3612 

38oo 

3988 

4176 

4363 

455 1 

4739 

4926 

5i i3 

53oi 

188 

232 

5488 

56 7 5 

5862 

6049 

6236 

6423 

6610 

6796 

6983 

7169 

187 

233 

7356 

7542 

7729 

79 l5 

8101 

8287 

8473 

86D9 

8845 

go3o 

186 

234 

9216 

9401 

9587 

9772 

9953 

•Mi 

•328 

•513 

•698 

•883 

i85 

235 

371068 

1253 

i43 7 

1622 

j 806 

199 1 

2i 7 5 

236o 

2544 

2728 

184 

236 

2912 

3096 

3280 

3464 

3647 

383i 

4015 

4198 

4382 

4565 

184 

237 

4748 

4932 

5i 15 

5298 

548i 

5664 

5846 

6029 

6212 

6394 

1 83 

238 

6577 

6759 

6942 

7124 

7 3o6 

7488 

7670 

7862 

8o34 

8216 

182 

239 

83 9 8 

858o 

8761 

8943 

9124 

93o6 

9487 

9668 

9849 

••3o 

181 

240 

380211 

o3g2 

o5 7 3 

o 7 54 

0934 

1115 

1296 

1476 

1 656 

1 83 7 

181 

241 

2017 

2197 

23 77 

255 7 

2737 

2 9H 

3097 

3277 

3456 

3636 

180 

242 

38i5 

3996 

4174 

4353 

4533 

4712 

4891 

5o 7 o 

5249 

5428 

179 

243 

56o6 

5 7 85 

6964 

6142 

6321 

6499 

6677 

6856 

7 o 34 

7212 

178 

244 

7390 

7 568 

7746 

7923 

8101 

8279 

8456 

8634 

8811 

8989 

178 

245 

9166 

9343 

9620 

9698 

9 8 7 5 

•*5i 

•228 

•4o5 

•582 

•709 

177 

246 

3gog35 

1112 

1288 

1464 

1641 

1817 

1993 

2169 

2345 

2521 

176 

247 

2697 

2873 

3o48 

3224 

3400 

35 7 5 

3 7 oi 

3926 

4101 

4277 

176 

248 

4452 

4627 

4802 

4977 

5152 

5326 

55oi 

6676 

585o 

6025 

175 

249 

6199 

63 7 4 

6548 

6722 

6896 

7071 

7245 

7419 

7592 

7766 

174 

25o 

397940 

8114 

8287 

8461 

8634 

8808 

8981 

9154 

9328 

9501 

173 

25i 

9674 

9847 

••20 

• 192 

•365 

•538 

•711 

•883 

io56 

1228 

173 

252 

401401 

i5 7 3 

1745 

1917 

2089 

2261 

2433 

26o5 

2777 

2949 

172 

253 

3121 

3292 

3464 

3635 

3807 

3978 

4Ug 

4320 

4492 

4663 

171 

254 

4834 

5oo5 

5i 7 6 

5346 

55i 7 

5688 

5858 

6029 

6199 

63 7 o 

171 

255 

654o 

6710 

6881 

7 o5i 

7221 

7391 

7 56i 

7731 

7901 

8070 

170 

256 

8240 

8410 

85 79 

8749 

8918 

9087 

9207 

9426 

9595 

9764 

169 

257 

9933 

•102 

•271 

•44o 

®6oo 

*777 

•946 

11 14 

1283 

1461 

169 

258 

411620 

1788 

1956 

2124 

2290 

2461 

2629 

2796 

2964 

3 i3a 

168 

259 

33oo 

3467 

3635 

38o3 

3970 

4i3 7 

43 05 

4472 

4639 

4806 

167 

260 

414973 

5i4o 

53o 7 

5474 

5641 

58o8 

5974 

6141 

63o8 

6474 

167 

261 

6641 

6807 

6973 

7 ‘39 

7 3o6 

7472 

7638 

7804 

7970 

8135 

166 

262 

83oi 

8467 

8633 

8798 

8964 

9129 

9295 

9460 

9625 

9791 

j 65 

263 

9956 

•121 

• 286 

•431 

•616 

•781 

•945 

1110 

i2 7 5 

1439 

1 65 

264 

421604 

1788 

iq 33 

2097 

2261 

2426 

2690 

2754 

2918 

3o82 

164 

265 

3246 

3410 

3074 

3737 

3901 

4o65 

4228 

4392 

4555 

4718 

164 

266 

4882 

5o45 

5208 

5371 

5534 

5697 

586o 

6023 

6186 

634o 

1 63 

267 

6511 

6674 

6836 

6999 

7161 

7324 

7486 

7648 

7811 

7973 

165 

268 

8135 

8297 

845q 

8621 

8 7 83 

8944 

9106 

9268 

9429 

9691 

162 

269 

9752 

9914 

•* 7 3 

•236 

•3 9 8 

•559 

° 7 20 

•881 

1042 

1203 

161 

270 

431364 

1 525 

i685 

1846 

2007 

2167 

23a8 

2488 

2649 

2809 

161 

271 

272 

2969 

4369 

3i3o 

4729 

3290 

4888 

345o 

5o48 

36io 

6207 

3770 

536 7 

3930 

5d26 

4090 

5685 

4249 

5844 

4409 

6004 

160 

159 

273 

6i63 

6322 

6481 

6640 

6708 

6957 

7116 

7275 

7433 

7592 

i5o 

274 

77 5i 

79°9 

8067 

8226 

8384 

8542 

8701 

885 9 

9017 

9175 

158 

276 

9333 

9491 

9648 

9806 

9964 

•122 

•279 

•437 

®5 9 4 

•7 52 

1 58 

276 

440909 

1066 

1224 

i38i 

1538 

1695 

1852 

2009 

2166 

2323 

157 

277 

2480 

2637 


2950 

3106 

3263 

3419 

35 7 6 

3 7 32 

388g 

167 

278 

4o45 

4201 

4337 

45i3 

4669 

4826 

4981 

513 7 

5293 

5449 

156 

279 

56o4 

5 7 6o 

5915 

6071 

6226 

6382 

653 7 

6692 

6848 

7 oo3 

1 55 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 























































A TABLE OF LOGARITHMS FROM 1 TO 10.000. § 


fs. 


5 

a 

3 

4 

5 

<6 

7 

8 

9 

D. 

280 

! 447*158 

73 1 3 

7468 

7628 

7778 

7 9 33 

8088 

8242 

8397 

8552 

1 55 


1 8706 

8861 

90.1 5 

9170 

9324 

9478 

• 9 633 

9787 

9941 

*•95 

1 54 



0007 

OJU 

©S 65 

■1018 

1172 

1326 

1479 

1 633 

1 54 

283 

1786 

1940 

2093 

2247 

2400 

2553 

2706 

2809 

3 oi 2 

3 1 65 

i 53 s 

284 

33 18 

3471 

3624 

3 777 

3 g 3 o 

4082 

4235 

4387 

4540 

4692 

1 53 - 

i:yj 

4845 

4997 

5 i 5 o 

53 o 2 

5454 

56 o 6 

5708 

5910 

6062 

6214 

i 5 i 

j 280 

6366 

65 i 8 

6670 

6821 

6973 

7*25 

7276 

7428 

7 5 79 

7731 

102 


7882 

8 o 33 

8184 

8336 

8487 

8638 

8789 

8940 

9091 

9242 

1 5 1 

j 288 

9892 

9543 

9694 

9845 

9995 

•146 

•296 

•447 

• 5 9 7 

•748 

1 5 1 

289 

460898 

1048 

1198 

1348 

*499 

1649 

*799 

1948 

2098 

2248 

i 5 e 

290 

462898 

2548 

2697 

2847 

2997 

3 i 46 

3296 

3445 

35 g 4 

3744 

i 5 o> 

j 291 

3898 

4042 

4 l 

4340 

4490 

4639 

4788 

4 9 36 

5 o 85 

5234 

149 

292 

5383 

5532 

568 o 

5829 

5 977 

6126 

6274 

6423 

6571 

6719 

i 4 9 . 

293 

6868 

7016 

7164 

7312 

7460 

7608 

7756 

7904 

8 o 5 a 

8200 

1 48 ! 

•294 

8347 

8495 

8643 

8790 

8 9 38 

9 o 85 

9233 

9 38 o 

9527 

9675 

148s 

295 

9822 

9969 

®i 16 

°s 63 

® 4 io 

•557 

•704 

• 85 i 

•998 

1 145 

147 - 

296 

471292 

1438 

•1 585 

1732 

1878 

2025 

2171 

23 18 

2464 

2610 

146' 

297 

27D6 

2003 

3 o 49 

3195 

3341 

3487 

3633 

3779 

3925 

4071 

146 

298 

4216 

4362 

45 o 8 

4653 

4799 

4944 

5090 

5235 

538 i 

55 s 6 

146 

2 99 

5671 

58 i 6 

5962 

6107 

6202 

6897 

6542 

6687 

6832 

6976 

14T 

j 3 oo 

477121 

7266 

74 .li 

7555 

7700 

7844 

7989 

81 33 

8278 

8422 

145 ' 

j 3 oi 

8566 

8711 

8855 

8999 

9143 

9287 

943 1 

9575 

9719 

9 863 

1 44 ' 

j 302 

480007 

oi 5 'i 

0294 

0438 

o 582 

0725 

0869 

1012 

1 1 56 

1299 

144 ; 

3 o 3 

1443 

1 586 

1 1729 

1872 

2016 

2 l 5 9 

2302 

2445 

2588 

2731 

143 

j 3 o 4 

2874 

3 oi 6 

3 1D9 

33o2 

3445 

3587 

3730 

3872 

401 5 

4 i 57 

143 ; 

] 3 o 5 

43 00 

4442 

4585 

4727 

4869 

5 oi 1 

5153 

5295 

5437 

5579 

142 

j 3 06 

5721 

5863 

6 oo 5 

6147 

6289 

643 o 

6572 

6714 

6855 

6997 

142! 

| 3 °7 

7iS8 

7280 

7421 

7563 

7704 

7845 

7986 

8127 

8269 

8410 

141 

j 3 o 8 

855 i 

8692 

8833 

8974 

9114 

9255 

9 3 9 6 

9537 

9 6 77 

9818 

141 

J 3 c >9 

9958 

6 *99 

•239 

« 38 o 

•520 

•661 

®8oi 

•941 

1081 

1222 

140 

j 3 io 

491362 

i 5 o 2 

1642 

1782 

1922 

2062 

2201 

234 * 

2481 

2621 

140 

3 11 

2760 

2900 

3 040 

3179 

3319 

3458 

35 9 7 

3787 

3876 

4 oi 5 

i 3 9 ' 

3 12 

4*55 

4594 

4433 

4572 

4711 

485 o 

4989 

5 is 8 

5267 

5406 

i 3 o. 

3 1 3 

5544 

5683 

5822 , 

5960 

6099 

6238 

6376 

65 1 5 

6653 

6791 

i 3 9 

3 14 

6980 

7068 

7206 

7344 

7483 

7621 

77 5 9 

7897 

8 o 35 

8173 

I 38 ; 

3 1 5 

83 11 

8448 

8586 

8724 

8862 

8999 

9 1 37 

9275 

9412 

9 55 o 

138 " 

3 r 8 

9687 

9824 

9962 

®« 99 

•236 

•874 

« 5 i 1 

•648 

®785 

•922 

i3 7 , 

3 17 

5 o1069 

1196 

1333 

1470 

1607 

1744 

1880 

2017 

21 54 

2291 

i 3 7 

3 18 

2427 

2564 

2700 

2837 

2973 

3 109 

3246 

338 a 

35 i 8 

36 d 5 

1 36 

319 

3 79 i 

3927 

4©63 

4199 

4335 

4471 

4607 

4743 

4878 

5 qi 4 

1 36 

320 

5 o 5 i 5 o 

5 s 86 

5421 

5557 

5693 

58 s 8 

5 9 64 

6099 

6 s 34 

6370 

i 36 ; 

321 

65 e 5 

6640 

6776 

6911 

7046 

7181 

781*6 

745 i 

7 586 

77.21 

1 35 

322 

7856 

799 1 
9337 

8126 

8260 

83 9 5 

853 o 

8664 

8799 

8934 

9068 

i 35 | 

323 

9208 

9471 

9606 

974 o 

9874 

®o« 9 

•i 43 

•277 

•411 

1 34 

324 

5 io 545 

0679 

o 8«3 

0947 

1081 

5 21 5 

1 349 

1482 

1616 

1750 

i 34 

323 

1 883 

2017 

2 l 5 l 

2284 

2418 j 

255 

2684 

2818 

2951 

3 o 84 

; 3 j 

326 

32 t 8 

335 1 

3484 

3617 

3 ~i 5 o ; 

3883 

4016 

4149 

4282 

44 i 4 

1 33 

327 

4548 

4681 

48 i 3 

4946 

5 o 79 j 

5211 

5344 

5476 

5609 

5741 

i 33 ; 

328 

58 7 4 

6006 

6139 

6271 

64 o 3 

6535 

6668 

6800 

6 q 32 

7064 

1 3 2 i 

329 

7196 

7328 

7460 

7592 

7724 

7 855 

7987 

8119 

8 s 5 i 

8382 

l 32 | 

33 o 

5 i 85 i 4 

864 $ 

6777 

8909 

9040 

9171 

9 3 o 3 

9434 

q 566 

9697 

i 3 i, 

33 * 

9828 

9959 

0*90 ! 

®22I 

•353 

•484 

• 6 i 5 

®745 

•876 

1007 

i 3 i 

j 332 

521 i 38 

1269 

i4eo | 

i 53 o 

1661 

1792 

1922 

2 o 53 

21 83 

2314 

1 3 1 

333 

2444 

2673 

2705 , 

2835 

2966 

3096 

3226 

3356 

3486 

36 i 6 

i 3 o; 

334 

3746 

3876 

4006 

4 i 36 

4266 

43 9 6 

4626 

4656 

4785 

491 5 

i 3 o 

335 

5 o 45 

5174 

53 o 4 

5434 

5563 

56 o 3 

5822 

5 g 5 i 

6081 

6210 

129 

! 336 

6339 

6469 

65 o 8 

6727 

6856 

6985 

7114 

7243 

7372 

75 oi 

129 

33 7 

7630 

7759 

7888 

8016 

8 t 45 

8274 

8402 

853 1 

8660 

8788 

!2Q 

338 

8917 

9045 

9 T 74 

9302 

9 43 o 

9 55 9 

9687 

9815 

9943 

•*72 

128 

339 

53o2oo 

0328 

0456 

o 584 

0712 

0840 

0968 

1096 

1223 

1 35 1 

128 

j N. 

■L 

0 

1 

2 

3 

4 

5 

6 

7 1 

8 

9 

D. 

—»■ 1—< 
































































































6 


A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

0 

1 

2 

3 

4 

5 

6 

| 7 

8 

] 

9 

j 340 

53 i 479 

1607 

1734 

1-862 

1990 

2117 

2245 

| 2372 

2300 

2627 

[341 

2754 

2882 

3009 

3 i 36 

3264 

3391 

35 1.8 

3643 

3772 

3899 

! 34a 

4026 

4i53 

4280 

4407 

4534 

4661 

47^7 

4914 

5 o 4 i 

5167 

343 

5294 

5421 

5547 

56 7 4 

58 co 

5927 

6 o 53 

6180 

63 o 6 

6482 

! 344 

6558 

6685 

6811 

6937 

7063 

7189 

781 5 

7441 

7067 

7693 

345 

7819 

7945 

8071 

8197 

8322 

8448 

8374 

8699 

8825 

8901 

i 346 

9076 

9202 

9327 

9432 

9378 

97 o3 

9829 

99^4 

*•79 

• 2*>4 

347 

5 '{ 03*9 

0455 

o 58 o 

0705 

o 83 o 

0935 

1080 

120*5 

i 33 o 

1454 

, 348 

1579 

1704 

1829 

1953 

2078 

2203 

23 27 

2452 

2576 

2701 

! 349 

*825 

2960 

30.74 

3199 

3323 

3447 

3371 

3696 

3820 

*944 

I 35 o 

J44068 

4192 

43 1.6 

444 ° 

4564 

4688 

4812 

4986 

5 o 6 o 

5 i 83 

35 1 

5307 

543i 

5555 

3678 

5802 

3923 

6049 

6172 

6296 

6419 

1 352 

6543 

6666 

6789 

6913 

7o36 

7159 

7282 

74o5 

7629 

7632 

353 

7775 

7898 

8021 

8144 

8267 

8389 

85 i 2 

8635 

8768 

8881 

! 354 

9003 

9126 

9249 

9371 

9494 

9616 

9739 

9861 

9984 

•1.06 

355 

550228 

o 35 i 

0473 

©596 

0717 

0840 

0962 

1084 

1206 

1328 

| 356 

i45o 

1672 

1694 

1816 

1938 

2060 

2181 

23 o 3 

2426 

2347 

1 357 

2668 

2790 

2911 

3 o 33 

3 1 55 

3276 

3398 

35 i 9 

364 o 

3762 

j 358 

3883 

4004 

4126 

4247 

4368 

4489 

4610 

473i 

4832 

4973 

j 359 

6094 

52 i 5 

5336 

5457 

5578 

5699 

5820 

8940 

6061 

6182 

| 36 o 

5563 o 3 

6423 

6644 

6664 

6785 

6905 

7026 

7146 

7267 

7387 

| 36 1 

7 5 o 7 

7627 

7748 

7868 

7988 

8108 

8228 

8349 

8469 

8089 

1 362 

8709 

8829 

8943 

9068 

9188 

9808 

9428 

9548 

9667 

9787 

1 363 

9907 

••26 

•146 

•265 

•385 

• 5 o 4 

•6*4 

•743 

•863 

•982 

1 364 

56 i101 

1221 

i34o 

1469 

i5 7 8 

1698 

1817 

1936 

2o55 

2174 

i 363 

2293 

2412 

253i 

265o 

2769 

2887 

3 oo 6 

3 l 23 

3*44 

3362 

j 366 

3481 

36 00 

3718 

3837 

3903 

4074 

4192 

4311 

4429 

4348 

| 367 

4666 

4784 

4903 

5021 

5i39 

5287 

5376 

5494 

5612 

6730 

: 368 

5848 

6966 

6084 

6202 

6320 

6437 

6555 

6673 

6791 

6909 

369 

7026 

7144 

7262 

7379 

7497 

7614 

773 * 

7849 

7967 

8084 

370 

568202 

83 i 9 

8436 

8554 

8671 

878a 

8905 

9023 

9140 

9257 

371 

9374 

9491 

9608 

9725 

9842 

9959 

••76 

•193 

•309 

•426 

372 

570643 

0660 

0776 

0893 

1010 

1126 

1243 

1359 

1476 

1392 

| 373 

1709 

1826 

1942 

2038 

2174 

2291 

2407 

2523 

2639 

2700 

374 

2872 

2988 

3io4 

32 20 

3336 

3452 

3568 

3684 

3800 

3915 

375 

4o3i 

4147 

4263 

4379 

4494 

4610 

4726 

4841 

4937 

5oj2 

376 

5 i 88 

53 o 3 

5419 

5534 

565 o 

5 j 6>5 

588 o 

5qq6 

6111 

6226 

3 77 

634 1 

6457 

6572 

6687 

6802 

6917 

7082 

7 U 7 

7262 

7377 

378 

7492 

7607 

7722 

o 836 

7931 

8066 

8181 

8293 

84 »o 

8020 

379 

8639 

8734 

8868 

8 9 83 

9097 

9212 

9326 

9441 

9555 

9669 

: 3 80 

579784 

9898 

••12 

•126 

•241 

•355 

•469 

•583 

•697 

•811 

38 i 

580925 

loJg 

11 53 

1267 

i 38 i 

i4o5 

1608 

1722 

1 836 

19O0 

382 

2 o 63 

2177 

2291 

2404 

25 18 

2631 

2745 

2858 

2972 

3o85 

383 

3 i 99 

33 i 2 

34*6 

3539 

3652 

3 -j 65 

3879 

3992 

4 io 5 

4218 

384 

433 1 

4444 

4557 

4670 

4783 

4896 

3009 

5 l 22 

5235 

5348 

385 

5461 

5574 

5686 

5799 

5912 

6024 

6137 

6250 

636*2 

6473 

386 

6587 

6700 

6812 

6923 

7037 

7149 

7262 

7374 

7483 

? s 99 

387 

77 11 

7823 

7 9 35 

8047 

8160 

8272 

8384 

8496 

8608 

8/20 

388 

8832 

8944 

9o56 

9167 

9279 

9391 

95o3 

96 i 5 

9726 

9838 

389 

9960 

•®6i 

*ij 3 

•284 

•396 

•607 

•619 

•730 

•842 

•903 

890 

591065 

1176 

1287 

i3 99 

i5io 

1621 

1732 

1843 

1955 

2066 

391 

2177 

2288 

23 99 

25io 

2621 

2782 

2843 

2934 

3064 

3ij5 

392 

3286 

33 9 7 

35 o 8 

36iS 

3729 

3840 

3950 

4o6i 

4171 

4282 

393 

4393 

45o3 

4614 

4 734 

4834 

4945 

5 o 55 

5 1 65 

5276 

5386 

394 

5496 

56 o 6 

3717 

5827 

5937 

6047 

6157 

6267 

6377 

6487 

396 

6597 

6707 

6817 

^ 9*7 

7037 

7146 

7226 

7366 

7476 

7586 

396 

7695 

7806 

79*4 

8024 

81 34 

8243 

8353 

8462 

857 2 

8681 

3 97 

8791 

8900 

9009 

9119 

9228 

9337 

9446 

9556 

9666 

9774 

398 

9883 

999 2 

•101 

•210 

•Jig 

•428 

•537 

•646 

• 7 55 

•864 

399 

600973 

1082 

1191 

I299 

1408 

1317 

1625 

1734 

1843 

1951 

L T . 

1 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 


IX 

i*8 

127 

127 

1*6 

126 

126 

125 

120 
125 
124 

124 

124 

123 
123 
1*3 
1 2-2 
122 

121 
121 
121 

120 
120 
120 
119 
119 
I I 9 
1 I 9 
<l8 
ll8 
ll8 

11 1 

117 

» »7 
116 
ll6 

116 
n 5 
no 
11 5 

114 

114 
114 
114 
1 13 
1 13 
u 3 

112 
112 
112 
m 

m 

! 1 I 
HI 
1 10 
I 10 
1 10 
1 10 
109 
109 
109 

D. 












































































A TABLE OF LOGARITHMS FROM 1 TO 10,000- 7 


j»- -- 

! N. 

0 

a 

2 

3 

4 

5 

6 

7 

8 

9 

d. : 

4oo 

602060 

2169 

2277 

2386 

i 4 9 4 

26®3 

2711 

2819 

2928 

3 o 36 

108! 

401 

3 144 

3253 

336 1 

3469 

3577 

3686 

3794 

3902 

4010 

4118 

108' 

402 

4226 

4334 

4442 

455 o 

4658 

4766 

4874 

4982 

5 o 8 9 

5197 

108' 

j 4 o 3 

53 o 5 

54 i 3 

DD21 

5628 

5 7 36 

5844 

0901 

6009 

6166 

6274 

108 

404 

638 i 

6489 

6696 

6704 

6811 

6919 

7026 

7 i 33 

7241 

7348 

107 

40 5 

7455 

7562 

l66g 

7777 

7884 

799 1 

8098 

8205 

83 12 

8419 

107 

406 

8326 

8633 

8740 

8847 

8 9 54 

9061 

9*67 

9 2 74 

9 38 i 

9488 

107 

407 

9394 

9701 

9808 

9914 

••21 

•128 

•234 

•341 

•447 

•554 

107 

408 

610660 

0767 

0873 

0979 

J086 

1192 

1298 

i4od 

1 5 i 1 

1617 

106 

409 

1723 

1829 

1936 

2042 

2148 

2254 

236 o 

2466 

2572 

2678 

io6l 

410 

612784 

2890 

2996 

3 ig 2 

3207 

33 j 3 

3419 

3525 

363 o 

3736 

106 

411 

3842 

3947 

4 o 53 

4169 

4264 

4370 

4475 

458 1 

4686 

4792 

106 

\ 412 

4897 

5 oo 3 

5 108 

02 13 

53 19 

5424 

5529 

5634 

5740 

5845 

io 5 | 

j 4 * 3 

59 DO 

6 o 55 

6160 

6265 

6370 

6476 

658 1 

6686 

6790 

68 9 5 

io 5 < 

i 4 i 4 

7000 

7106 

7210 

73 15 

7420 

7525 

7629 

7734 

? 83 9 

7943 

I 05 1 

1 4 i 5 

8048 

81 53 

825 7 

8362 

8466 

8571 

8676 

8780 

8884 

8989 

io 5 

j 416 

9093 

9198 

9802 

9406 

9 5 n 

9615 

9719 

9824 

9928 

••32 

104 

417 

620136 

0240 

o 344 

0448 

o 552 

g 656 

0760 

0864 

0968 

1072 

1 o 4 | 

- 4 i» 

1176 

1280 

1384 

1488 

j 5 9 2 

1695 

2799 

i 9 o 3 

2007 

2110 

104 

j 41 9 

2214 

23 i 8 

2421 

2525 

2628 

27 32 

2835 

2939 

8042 

3 i 46 

104 

j 420 

623249 

3353 

34^6 

355 9 

3663 

3766 

3869 

3973 

407-6 

4179 

ig 3 

421 

4282 

4385 

4488 

45 9 1 

46 9 5 

4798 

4901 

5004 

6107 

5210 

io 3 ! 

422 

531 2 

54 1 5 

5528 

5621 

6724 

5827 

5929 

6 o 32 

6 i 35 

6238 

1 o 3 i 

423 

6340 

6443 

6546 

6648 

6751 

6853 

69 56 

7 o 58 

7161 

7263 

io 3 l 

424 

7366 

7468 

75 7 2 

7673 

7775 

7878 

7980 

8082 

81 85 

8287 

102 

423 

838 9 

849J 

85 9 3 

860D 

8797 

8900 

9002 

9104 

9206 

9 3 o 8 

1021 

426 

9410 

9612 

9613 

97*5 

9817 

9919 

••21 

•123 

•224 

• 3 a 6 

102; 

! 427 

63o428 

o 53 o 

o 63 i 

0733 

o 835 

0936 

io 38 

n 3 9 

1241 

1 342 

102 [ 

428 

1444 

i 545 

1647 

1748 

1849 

1951 

2052 

21 53 

2255 

2356 

101! 

429 

24D7 

2559 

2660 

2761 

2862 

2963 

3 o 64 

3 i 65 

3266 

336 7 

IOl 

43 o 

633468 

356 q 

3670 

3 77 i 

3872 

3 97 3 

4074 

4176 

4276 

4376 

100; 

431 

4477 

4D78 

4679 

4779 

4880 

4981 

5 o 8 i 

5182 

5283 

5383 

iooj 

432 

5484 

5584 

568 o 

5 7 85 

5886 

D986 

6087 

6187 

6287 

6388 

100' 

433 

6488 

6588 

6688 

6789 

6889 

6989 

7089 

7189 

7290 

l 3 g° 

100; 

434 

7490 

i 5 q° 

7690 

779 ° 

7 V 

799 ° 

8090 

8190 

8290 

838 9 

99 

435 

8489 

8589 

8689 

8789 

8888 

8988 

9088 

9188 

9 2 «7 

9387 

99 , 

436 

9486 

9586 

9686 

9780 

9 88 d 

9984 

••84 

•1 83 

•:83 

•382 

99 

i 437 

640481 

o 58 i 

0680 

0779 

0879 

0978 

1077 

H 77 

1276 

i 3-]5 

99 

438 

1474 

i 573 

1672 

1771 

1871 

1970 

2069 

2168 

2267 

2366 

99 

{ 439 

2465 

25 W 

2662 

2761 

2860 

29D9 

3 o 58 

3 i 56 

3255 

3354 

99 ! 

440 

643453 

355 i 

365 o 

3749 

3847 

3946 

4044 

4 U 3 

4242 

434 o 

9 g | 

44 i 

4439 

4537 

4636 

4734 

4832 

4 9 3 i 

5o2 9 

5127 

5226 

5324 

98 j 

• 442 

5422 

5521 

5619 

5717 

58 i 5 

5913 

6011 

6110 

6208 

63 o 6 

981 

443 

6404 

65 o 2 

6600 

6698 

6796 

6894 

6992 

7089 

7 *S 7 

7285 


444 

445 

7383 

836 o 

748 i 

8458 

7579 

8555 

7676 

8653 

777 4 

8760 

7872 

8848 

7960 

8945 

8067 

9043 

8165 

9140 

8262 

9237 

98 1 
97 

446 

9335 

943 a 

9 53 o 

9627 

9724 

9821 

9919 

•®i6 

•1 13 

•210 

97! 

447 

65 o 3 o 8 

o4oD 

0502 

0099 

0696 

o 79 3 

0890 

0987 

1084 

1181 

97 i 

448 

1278 

i 375 

1472 

1589 

1666 

1762 

1809 

1956 

2 o 53 

2l5o 

97 ! 

449 

2246 

2343 

2440 

2536 

2633 

2730 

2826 

2923 

3 oi 9 

3 i 16 

97 

45o 

653223 

33 oq 

34 o 5 

35 o 2 

35 9 8 

36 9 5 

3791 

3888 

3984 

408c 

96 

i 451 

4177 

4273 

4369 

4465 

4562 

4658 

4754 

48 5 o 

4 9 46 

5 o 42 

9 a 

452 

5138 

5235 

5331 

5427 

5523 

56 19 

5715 

58 io 

5906 

6002 

96 1 

453 

6098 

6194 

6290 

6386 

6482 

6077 

6673 

6769 

6064 

6960 

96; 

454 

7006 

71 52 

7 24 7 

7343 

7438 

7534 

7629 

7725 

7820 


9 ji 

455 

8021 

8107 

8202 

8298 

83 9 3 

8488 

8584 

8679 

« 77 4 

8870 


456 

8965 

9060 

91 55 

9 2 DO 

9346 

9441 

9536 

9 63 i 

9726 

9821 

9 5 ' 

457 

0016 

•• I I 

•106 

•201 

•296 

• 3 9 i 

•486 

•581 

•676 

•771 

9 §, 

458 

66086 5 

0960 

io 55 

i i 5 o 

1243 

i 339 

1434 

1520 

1623 

1718 

9 §i 

459 

i 8*3 

1907 

2002 

2096 

2191 

2286 

2 38 o 

2476 

2 56 9 

2663 

9 s : 

N. 

L 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

























































8 A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

. 

0 

r 

2' 

5 

4 

5 

6 

7 

8 

9 

D. 

i 460 

662758 

2852 

2947 

3 o 4 i 

3 1 35 

323 o 

3324 

3418 

35 n 

3607 

94 

461 

3701 

3795 

388 9 

3 9 83 

4078 

4172 

4266 

436 o 

4454 

4548 

94 

462 

4642 

4786 

483 o 

4924 

5 oi 8 

5 112 

6206 

5299 

53 9 3 

5487 

94 

463 

558 1 

5675 

5769 

5862 

5956 

6 o 5 o 

6143 

6237 

633 1 

6424 

94 

464 

65 18 

6612 

6706 

6799 

6892 

6986 

7079 

7173 

7266 

736 o 

9? 

465 

7453 

7046 

7640 

7733 

7826 

792c 

8 oi 3 

8106 

8199 

8293 

9 3 

466 

8386 

8479 

8572 

8665 

8759 

8852 

8945 

9088 

91 3 1 

9224 

9 3 

, 467 

' 93 1 7 

9410 

95 o 3 

9596 

9689 

9782 

9873 

9967 

••60 

• 1 53 

93 

468 

670246 

0339 

0431 

0024 

0617 

0710 

0802 

0895 

09S8 

1080 

93 1 

469 

1173 

1260 

1 358 

1 45 1 

i 543 

i 636 

1728 

1821 

1913 

2005 

9 3 j 

470 

672098 

2190 

2283 

2375 

2467 

256 o 

2652 

2744 

2836 

2929 

92' 

471 

3021 

3 11 3 

32 o 5 

3297 

3390 

3482 

3574 

3666 

3 j 58 

385 o 

92'i 

' 472 

3942 

4 o 34 

4126 

4218 

43 10 

4402 

4494 

4586 

4677 

4769 

92 i 

; 473 

4861 

4953 

0040 

5 1 3 7 

5228 

5320 

5412 

55 o 3 

5596 

5687 

92 j 

j 474 

5778 

6870 

6962 

6 o 53 

6145 

6236 

6328 

6419 

651 1 

6602 

92 

1 475 

6694 

6785 

6876 

6068 

7089 

71 5 1 

7242 

7333 

7424 

75 i 6 

9 1 

476 

7607 

7698 

7739 

7881 

7072 

8 o 63 

81 54 

8245 

8336 

8427 

9 1 

477 

85 18 

8609 

8700 

8791 

8882 

8973 

9064 

9 i 55 

9246 

9337 

91 

1 476 

9428 

95 1 9 

9610 

9700 

979 1 

9882 

997 3 

••63 

• 1 54 

•245 

9 1 

' 479 

68 o 336 

0426 

o 5 i 7 

0607 

0698 

0789 

0879 

0970 

1060 

11 5 i 

9 | 

480 

681241 

i 332 

1422 

1 5 1 3 

i 6 o 3 

1693 

1784 

1874 

1964 

2 o 55 

90 

' 4 ' 3 1 

2145 

2235 

2826 

2416 

25 o 6 

2596 

2686 

?777 

2867 

2957 

90 

; 482 

3 o 47 

3 137 

3227 

3817 

3407 

3497 

3587 

3677 

3767 

3857 

9 ° 

483 

3947 

4037 

4127 

4217 

4307 

4396 

4486 

4576 

4666 

4756 

901 

1 484 

4845 

4935 

D02D 

5 114 

6204 

5294 

5383 

5473 

5563 

5652 

o° 

485 

5742 

583 i 

D921 

6010 

6100 

6189 

6279 

6368 

6468 

6547 

89 

486 

6636 

6726 

68i 5 

6904 

6994 

7 o 33 

7172 

7261 

735 1 

744 o 

89 

487 

7529 

7618 

7707 

7796 

7886 

797 5 

8064 

81 53 

8242 

833 1 

89 i 

: 488 

8420 

8509 

8598 

8687 

8776 

8865 

8 9 53 

9042 

9131 

Q 220 

89 

: 489 

9309 

9398 

9486 

9073 

9664 

9 7 53 

9841 

9930 

••19 

•107 

89! 

i 490 

690196 

0285 

o 3 - j 3 

0462 

o 55 o 

o 63 q 

0728 

0816 

0905 

0993 

89 

491 

1081 

1170 

1258 

1847 

1435 

1324 

1612 

1700 

1789 

1877 

88 • 

492 

1965 

2 o 53 

2142 

2230 

23 18 

2406 

2494 

2583 

2671 

2759 

88 i 

! 493 

2847 

2935 

3 o 23 

311 1 

3 i 99 

3287 

3375 

3463 

3551 

363 9 

884 

494 

3727 

38 1 5 

3903 

3991 

4078 

4 i 66 

4234 

4342 

443 o 

4617 

88j 

j 495 

46 o 5 

4693 

4781 

4868 

4 g 56 

5 o 44 

5131 

5219 

5307 

5394 

88. 

! 496 

6482 

6369 

6687 

5744 

5832 

5919 

6007 

6094 

6182 

6269 

87! 

497 

6356 

6444 

653 1 

6618 

6706 

6 79 3 

6880 

6968 

7o55 

7142 

87! 

I 498 

7229 

7317 

74 o 4 

749 ' 

7578 

7665 

7702 

7839 

7926 

8014 

8? 

; 499 

8101 

6188 

8273 

8362 

8449 

8535 

8622 

8709 

8796 

8883 

87 

i 5 oo 

698970 

9 o 5 7 

9144 

923 l 

9317 

9404 

9 49 1 

9578 

9664 

975 1 

87 

5 oi 

9838 

9924 

••1 1 

**98 

•184 

•271 

•338 

•444 

• 53 1 

•617 

87 

D02 

700704 

° 79 ° 

0877 

0963 

io 5 o 

11 36 

1222 

1309 

1 3 q 5 

1482 

86. 

5 o 3 

1 568 

1604 

1741 

1827 

1913 

1999 

2086 

2172 

2208 

2344 

86; 

! 5 o 4 

243 1 

25 17 

26 o 3 

2689 

2773 

2861 

2947 

3 o 33 

3 i 19 

32 o 5 

86 

, 5 o 5 

3201 

3377 

3463 

3349 

3635 

3721 

3807 

3898 

3979 

406 5 

86- 

5 o 6 

41 5 1 

4236 

4322 

4408 

4494 

4579 

4665 

4761 

4837 

4922 

86 

507 

5 oo 8 

5094 

5179 

5265 

535 o 

5436 

5522 

5607 

56 g 3 

5778 

86 

! 5 o 8 

5864 


6 o 35 

6120 

6206 

6291 

6376 

6462 

6547 

6632 

85 

: 509 

6718 

6808 

6888 

6974 

7059 

7*44 

7229 

73 x 5 

7400 

7485 

85 

5 io 

707570 

7655 

7740 

7826 

79 11 

7996 

8081 

8166 

825 i 

8336 

85 

5 u 

8421 

85 o 6 

8691 

8676 

8761 

8846 

8931 

9016 

9100 

9185 

85 

5 r 2 

9270 

9355 

9440 

9624 

9609 

9694 

9779 

9863 

9948 

••33 

85 

| 5 1 3 

710117 

0202 

0287 

0371 

0456 

0540 

0625 

0710 

0794 

0879 

85 - 

5 14 

0963 

1048 

1 132 

1217 

i 3 oi 

1 385 

1470 

1 554 

1609 

1723 

84 

5 1 5 

1807 

1892 

1976 

2060 

2144 

2229 

23 1 3 

2897 

2481 

2566 

84. 

5 16 

265 o 

2734 

2818 

2902 

2986 

3070 

3 1 54 

3238 

3323 

3407 

84 

■ 3*2 

3491 

3575 

8669 

3742 

3826 

3910 

3 994 

4078 

4162 

4246 

84. 

5 i 8 
! ^19 

43 3 o 
5167 

44 i 4 
525 1 

4497 

5335 

458 1 

5418 

4665 

55o2 

4749 - 

5586 

4833 

5669 

4916 

5753 

5 000 
5836 

5 o 84 

5920 

841 

84, 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

a 

9 

IX 
























































A TABLE OF LOGARITHMS FROM 1 TO 10,000. 9 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1>. 

520 

716008 

6087 

6170 

6254 

6337 

6421 

65o4 

6588 

6671 

6754 

83 

D2I 

6838 

6921 

7004 

7088 

7*7* 

7254 

7338 

7421 

7 5o4 

7% 

83 

522 

767* 

7734 

7837 

7920 

8oo3 

8086 

8169 

8253 

8336 

8419 

83 

523 

85o2 

8585 

8668 

8751 

8834 

89*7 

9000 

9 o83 

9165 

9248 

83 1 

524 

9 33i 

9414 

9497 

9580 

9 663 

9745 

9828 

9911 

9994 

•*77 

83 

525 

7 2oi5 9 

0242 

o325 

0407 

o4 9 o 

0573 

o655 

0738 

0821 

o 9 o3 

831 

526 

0986 

1068 

1151 

1233 

1316 

i3 9 8 

1481 

1563 

1646 

1728 

82 j 

527 

1811 

1893 

1975 

2o58 

2140 

2222 

23o5 

2387 

2469 

2552 

82! 

528 

2634 

2716 

2798 

2881 

2 9 63 

3o45 

3127 

3209 

32 9 i 

33 7 4 

8a! 

329 

3456 

3538 

3620 

3702 

3 7 84 

3866 

3948 

4o3o 

4112 

4l 9 4 

Sal 

53o 

724276 

4358 

444o 

4522 

4604 

4685 

4767 

4849 

4 9 31 

5oi3 

82 

531 

5o 9 5 

5176 

5258 

5340 

5422 

55o3 

5585 

5667 

5748 

583o 

82 

532 

5 9 I2 

5993 

6075 

6156 

6238 

632o 

6401 

6483 

6564 

6646 

82! 

533 

6727 

6809 

6890 

6972 

7o53 

7134 

7216 

7297 

7 3 79 

7460 

8 * 

534 

7541 

7623 

77°4 

7780 

7866 

7948 

8029 

8110 

8191 

8273 

81 

535 

8354 

8435 

85i6 

8097 

8678 

8739 

8841 

8922 

9 oo3 

9084 

81 

536 

9 i65 

9246 

9327 

9408 

9489 

9 5 7o 

9 65i 

9732 

9813 

9 8 9 3 

8i 

5 3 7 

9974 

••55 

®i36 

•217 

•298 

•3 7 8 

°45 9 

•540 

•621 

•702 

81 

538 

780782 

o863 

0944 

1024 

i io5 

1186 

1266 

1347 

1428 

i5o8 

81 

53 9 

i 58 9 

1669 

i 7 5o 

i83o 

1911 

1991 

2072 

2162 

2233 

2313 

8i 

54o 

732394 

2474 

2555 

2635 

2715 

2796 

2876 

2 9 56 

3o3 7 

3i 17 

80 1 

541 

3197 

3278 

3358 

3438 

3518 

35 9 8 

3679 

3709 

383 9 

39*9 

801 

542 

3 999 

4079 

4160 

4240 

4320 

4400 

4480 

456o 

4640 

4720 

80 

543 

4800 

4880 

4960 

5o4o 

5l20 

5200 

5279 

535 9 

5439 

5519 

80 

544 

55 99 

5679 

0709 

5838 

5918 

D998 

6078 

6157 

6237 

6317 

80 

545 

6397 

6476 

6556 

6635 

6715 

6795 

6874 

6954 

7034 

7113 

80 

546 

7 1 9 3 

7272 

7352 

7431 

7511 

73 9 o 

7 6 7° 

7749 

7829 

7908 

79 

547 

7987 

0067 

8146 

8225 

83o5 

8384 

8463 

8043 

8622 

8701 

79 

548 

8781 

8860 

8989 

9018 

9097 

9*77 

9 256 

9 336 

94*4 

949 3 

79 

549 

9672 

965i 

9781 

9810 

9889 

9968 

®°47 

•126 

®2o5 

•284 

79 

55o 

74o363 

0442 

0321 

0600 

0678 

0757 

o836 

0915 

0994 

1073 

79 

5 5i 

I i 52 

1230 

1809 

1388 

1467 

1D46 

1624 

1703 

178-! 

i860 

79 

552 

i 9 3 9 

2018 

2096 

2175 

2254 

2332 

2411 

2489 

2568 

2647 

79 

553 

2725 

2804 

2882 

2961 

3o3 9 

3118 

3196 

327 0 

3353 

3431 

781 

554 

35io 

3588 

3667 

8743 

3823 

3 9 02 

3 9 8o 

4o58 

4i36 

4215 

78] 

555 

42 9 3 

4371 

4449 

4528 

4606 

4684 

4762 

4840 

49*9 

4997 

78 

556 

5075 

5i53 

523i 

53o9 

5387 

5465 

5543 

5621 

5699 

5777 

78 

557 

5855 

5 9 33 

6011 

6089 

6167 

6245 

6323 

6401 

6479 

6556 

78 I 

558 

6634 

6712 

6790 

6868 

6943 

7023 

7101 

7*79 

7256 

7334 

78 

559 

74i2 

7489 

7567 

7643 

7722 

7800 

7878 

79 5o 

8o33 

8110 

78 

56o 

748188 

8266 

8343 

8421 

8498 

8676 

8653 

8731 

8808 

8885 

77 

561 

8 9 63 

9040 

9118 

9198 

9272 

9 35o 

9427 

9 5o4 

9 582 

9659 

77 

562 

9786 

9814 

9891 

9968 

®°43 

®123 

®200 

•277 

•354 

•431 

77 

563 

75o5o8 

q586 

0663 

0740 

0817 

0894 

°9 7 [ 

1048 

1125 

1202 

77 

564 

1279 

i356 

1433 

i5io 

1587 

1664 

1741 

1818 

i8 9 5 

1972 

77 

565 

2048 

2123 

2202 

2279 

2356 

2433 

2D0 9 

2586 

2663 

2740 

77 

566 

2816 

2893 

297 0 

3o47 

3123 

3200 

3277 

3353 

343o 

35o6 

77 

§67 

3583 

366o 

3786 

3813 

388 9 

3966 

4042 

4119 

4i 9 5 

4272 

77 

568 

4348 

4425 

45oi 

4578 

4654 

4730 

4807 

4883 

4960 

5o36 

76 

569 

5i 12 

5189 

5265 

5341 

5417 

6494 

5570 

5646 

5 7 22 

§799 

76 

5 io 

755875 

5951 

6027 

6io3 

6180 

6256 

6332 

6408 

6484 

656o 

76 

5 7 1 

6636 

6712 

6788 

6864 

6940 

7016 

7092 

7168 

7244 

7 320 

76 

572 

7896 

7472 

7548 

7624 

7700 

7773 

7861 

7927 

8oo3 

8079 

76 

573 

8o5 

823o 

83o6 

8382 

8438 

8533 

8609 

8685 

8761 

8836 

76 

374 

891 2 

8988 

9068 

9 i3 9 

9214 

9290 

9 366 

9 44* 

93*7 

9092 

76 

j 575 

9668 

9743 

9819 

9894 

9970 

••43 

® 121 

•196 

•272 

•347 

75 

576 

760422 

0498 

0873 

0649 

0724 

°799 

0875 

0930 

1025 

1101 

7 3 

* 577 

1176 

I2D1 

13 26 

1402 

1477 

1 002 

1627 

1702 

1778 

1853 

7 5 

1 578 

1028 

2003 

2078 

2153 

2228 

23o3 

23 7 8 

2453 

2529 

2604 


c' 

579 

2679 

2754 

2829 

2904 

2978 

3o53 

3128 

32o3 

3278 

3353 

7 5 

N. 

L.- 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

D. 


























































10 A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 


N. 

0 

I 

1 2 

1 

3 

4 

5 

6 

7 

8 

9 

1). 

58 o 

763428 

35 o 3 

3578 

3653 

3727 

38 o 2 

38 77 

3 9 52 

4027 

4101 

7 ^ 

58 1 

4176 

425 1 

4326 

44 oo 

4475 

455 o 

4624 

4699 

4774 

4848 

7 5 

582 

4923 

499 s 

5072 

5 1 47 

5221 

5296 

5370 

5445 

5520 

55 9 4 

7 $ 

583 

5669 

5743 

58 i 8 

58 9 2 

5966 

6041 

611 5 

6190 

6264 

6338 

74 

584 

6413 

6487 

6562 

6636 

67IO 

6785 

685 9 

6 9 33 

7007 

7082 

74 

585 

71 56 

723 o 

7304 

7379 

7453 

7527 

7601 

7675 

7749 

7823 

,4 

586 

7898 

7972 

8046 

8120 

8194 

8268 

8342 

8416 

8490 

8564 

*>4 

587 

8638 

8712 

8786 

8860 

8934 

9008 

9082 

91 56 

9280 

9803 

74 

588 

9 3 77 

945 i 

9 525 

9699 

9673 

9746 

9820 

9894 

9968 

••42 

74 

58 (p 

77011 5 

0189 

0263 

o 336 

0410 

0484 

0557 

o 63 i 

0705 

0778 

74 

590 

770852 

0926 

0999 

1073 

1146 

1220 

1298 

1367 

i 44 o 

i 5>4 

74 

691 

1 1087 

1661 

1734 

1808 

l88l 

1955 

2028 

2102 

2170 

2248 

73 

5 q 2 

2322 

2395 

2468 

2542 

26 i 5 

2688 

2762 

2835 

2908 

2981 

73 

5 9 3 

3 o 55 

3 J 28 

3201 

3274 

3348 

3421 

3494 

3567 

3 c> 4 o 

3713 

73 

5 9 4 

3786 

386 o 

3 9 33 

4006 

4079 

4 i 52 

4220 

4298 

4371 

4444 

7 3 

5 9 5 

4517 

4590 

4663 

4736 

4809 

4882 

4955 

5 o 28 

5 ioo 

5173 

73 

596 

5246 

531 9 

53 9 2 

5465 

5538 

56 io 

5683 

5756 

5829 

5902 

73 

5 97 

5974 

6047 

6120 

6193 

6260 

6338 

6411 

6483 

6556 

6629 

73 

598 

6701 

6774 

6846 

69 '9 

6992 

7064 

7137 

7209 

7282 

7354 

73 

5 99 

7427 

7499 

7 5 7 2 

7644 

77 1 7 

7789 

7862 

7934 

8006 

8079 

72 

600 

778*51 

8224 

8296 

8368 

8441 

8513 

8585 

8658 

8730 

8802 

72 

601 

8874 

8947 

9019 

9091 

91 63 

9236 

93 o 8 

9 38 o 

9452 

9024 

72 

602 

9596 

9669 

974 i 

9813 

9885 

9957 

••29 

•ioi 

•i 7 3 

•245 

72 

6 o 3 

780317 

0389 

0461 

o 533 

o 6 o 5 

0677 

0749 

0821 

0893 

0963 

72 

604 

1037 

1109 

11S1 

1253 

i 324 

1396 

1468 

1540 

1612 

1684 

72 

6 o 5 

1755 

1827 

1899 

I 97 I 

2042 

2114 

2186 

2258 

2329 

2401 

72 

606 

2473 

2544 

2616 

2688 

2 7 5 9 

283 1 

2902 

2974 

8046 

3 ii 7 

72 

607 

3 i 8 9 

3260 

3332 

34 o 3 

3475 

3546 

36 i 8 

368 o 

3761 

3832 

71 

608 

3904 

8973 

4046 

4 f 18 

4189 

4261 

4332 

44 o 3 

4470 

4546 

7 »* 

609 

4617 

4689 

4760 

483 1 

4902 

4974 

5 o 45 

5 i ?6 

0187 

525 9 

7 * 

610 

78533 o 

54 oi 

5472 

5543 

56 i 5 

5686 

5 7 37 

6828 

5899 

5970 

7 i 

611 

6041 

6112 

61 83 

6264 

6325 

6396 

6467 

6538 

6609 

6680 

71 

612 

6731 

6822 

68 9 3 

6964 

7o35 

7106 

7*77 

7248 

7819 

7390 

71 

61 3 

7460 

753 i 

7602 

7673 

7744 

7810 

7885 

7906 

8027 

8098 

7 * 

614 

8»68 

8239 

83 io 

838 i 

8451 

8522 

85 9 3 

8663 

8734 

8804 

7 * 

61 5 

8875 

8946 

9016 

9087 

9 ! 57 

9228 

9299 

9 36 9 

9440 

9610 

71 1 

616 

9681 

9651 

9722 

9792 

9-863 

9933 

• •• < 

*4 

•*74 

°*44 

* 2 l 5 

70 

617 

790285 

o 356 

0426 

0496 

0067 

0637 

0707 

0778 

0848 

0918 

70 

618 

0988 

1059 

1129 

11 99 

1269 

i 34 o 

i4ro 

*480 

* 55 o 

1620 

70 

619 

1691 

1761 

i 83 1 

1901 

1971 

2041 

Din 

2181 

2302 

2322 

7 ° 

620 

7923 q 2 

2462 

2532 

2602 

2672 

2742 

28r2 

2882 

2 9 52 

3022 

70 

621 

3092 

3 i 62 

323 i 

33 oi 

3371 

344 1 

35 11 

358 i 

365 1 

3721 

70 

622 

3790 

386 o 

3 9 3 o 

4000 

4070 

4139 

4209 

4279 

4349 

44 l 8 

7 C 

623 

4488 

4558 

4627 

4697 

4767 

4836 

4906 

4976 

5 o 40 

5 n 5 

70 

624 

5 i 85 

5254 

5324 

53 9 3 

5463 

5532 

56 o 2 

5672 

5741 

58 i 1 

70 

j 626 

588 o 

5 9 4 9 

6019 

6088 

61 58 

6227 

6297 

6366 

6436 

65 c 5 

69 

626 

65741 

6644 

6713 

6782 

6852 

6921 

6990 

7060 

7 i2 9 

7198 

69 

627 

7268 

7337 

7406 

? 4?5 

7545 

? 6 r 4 

7633 

7752 

7821 

7890 

60 

628 

7960 

8029 

8098 

8167 

8236 

83 o 5 

83?4 

8443 

85»3 

8582 

69 

! 629 

865 1 

8720 

8789 

8358 

8927 

8996 

9060 

9 i 34 

9 2 o 3 

9272 

69 

63 o 

799341 

9409 

9478 

9547 

9616 

9685 

9754 

9823 

9892 

9961 

69 

63 1 

800029 

0098 

0167 

0236 

o 3 o 5 

o 3 f 3 

0442 

o 5 i 1 

0080 

0648 

69 

632 

0717 

0786 

0854 

0923 

0992 

1061 

1129 

1198 

1266 

*335 

69 

633 

J 4 o 4 i 

1472 

1541 

1609 

1678 

•747 

i 8 i 5 

1884 

l 9 52 

2021 

69 

634 

2089 

21 58 

2226 

22 9 3 | 

2363 

2432 

25 oo 

2568 

2637 

2708 

60 

635 

2774 

2842 

2910 

-979 

3 o 47 

3 116 

3 1 84 

3252 

3321 

338 9 

68 

636 

3457 

3525 

3394 

3662 

3730 

3793 

3367 

3 9 35 

4008 

4071 

68 

63 7 

4139 

4208 

4276 

4344 

4412 

4480 

4548 

4616 

4685 

4?53 

68 

0J8 

4821 

4889 

4937 

5 o 25 

5093 

5 i 6 i 

5229 

5297 

5365 

5433 

68 

639 

55 oi 

5369 

5637 

5705 

5 77 3 

584 t 

5 9 o 8 

5976 

6044 

6112 

68 

N. 

*■- - .. 

0 

\ 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 



























































































A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 11 


r* ; 

I 0 

1 

— 

1 

2 

3 

4 

5 

6 

7 

8 

9 

B. 

640 

806180 

1 6248 

6316 

6384 

645 i 

6519 

658 7 

6655 

6723 

6790 

68 

641 

6858 

6926 

6994 

7061 

7129 

7197 

7264 

7332 

7400 

7467 

68 

542 

7535 

7603 

7610 

7738 

7806 

7873 

7941 

8008 

8076 

8143 

68 

643 

8211 

8279 

8346 

8414 

8481 

8649 

8616 

8684 

8761 

8818 

67 

644 

8886 

8 9 53 

9021 

9088 

gi56 

9228 

9290 

o358 

9425 

9492 

87 

645 

9560 

9627 

9694 

9762 

9829 

9806 

9964 

°»3i 

••98 

•i65 

87 

646 

8 io 233 

o3oo 

0367 

O434 

o5oi 

0569 

c63o 

0703 

0770 

0837 

87 

647 

0904 

°97 I 

1039 

1106 

1173 

i 1240 

1307 

1374 

1441 

15o8 

87 

648 

1376 

1642 

1709 

1776 

i 843 

1910 

1977 

2044 

2111 

2178 

87 

649 

2246 

2312 

23 79 

2443 

25l2 

2379 

2646 

2713 

278c 

2847 

87 

65o 

812913 

2980 

3o47 

3114 

3 i 8 i 

3247 

3314 

3381 

3448 

3514 

87 

(01 

3581 

3648 

3714 

3781 

3848 

3914 

3981 

4c 48 

4114 

4181 

87 

65'i 

4248 

4314 

4381 

4447 

4514 

458i 

4647 

4714 

4780 

4847 

67 

653 

4913 

4980 

5o46 

51 x 3 

5 i 79 

5246 

5312 

5378 

5445 

5511 

66 

654 

5578 

5644 

5711 

5777 

5843 

6910 

5976 

6042 

6109 

6175 

66 

655 

6241 

63o8 

6374 

6440 

65o6 

65-/3 

6639 

6705 

6771 

6838 

66 

656 

6904 

6970 

7036 

7102 

7169 

7235 

j3ci 

7367 

7433 

7499 

66 

667 

7365 

763 i 

7698 

7764 

j83o 

7896 

7962 

8028 

8094 

8160 

66 

658 

8226 

8292 

8338 

8424 

8490 

8336 

8622 

8688 

8754 

8820 

66 

659 

8885 

8931 

9 OI 7 

9083 

9*49 

92x5 

9281 

9346 

9412 

9478 

66 

660 

819644 

9610 

9676 

974 i 

9807 

9873 

99 3 9 

©•©/ 

09 -jo 

• 136 

66 

661 

820201 

0267 

o333 

0899 

0464 

o53o 

0693 

066: 

O727 

0792 

66 

662 

o858 

0024 

0989 

1033 

1120 

1186 

I 251 

1317 

i 382 

1448 

66 

663 

1514 

1879 

i 645 

1710 

1775 

1841 

1906 

1972 

2037 

2io3 

65 

664 

2168 

2233 

2299 

2364 

2480 

2496 

2360 

2626 

2691 

2766 

65 

665 

2822 

2887 

2932 

3oi8 

3o83 

3i48 

3 213 

3279 

3344 

3409 

65 

666 

3474 

3539 

36o5 

3670 

3j35 

3 800 

3865 

3930 

3996 

4061 

65 

667 

4126 

4191 

4256 

4321 

4386 

4451 

4316 

458 i 

4646 

4711 

65 

668 

4776 

4841 

4906 

4971 

5o36 

5 ioi 

5166 

3231 

5296 

536i 

65 

669 

5426 

5491 

5556 

5621 

5686 

5 7 5 i 

58.-5 

588o 

5945 

6010 

65 

670 

826075 

6140 

6204 

6269 

6334 

6399 

6464 

8528 

6693 

6658 

65 

671 

6723 

6787 

6852 

6917 

6981 

7046 

7111 

7175 

7240 

73o5 

65 

672 

7369 

7434 

7499 

7663 

7628 

7692 

77=>7 

7821 

7886 

7? 5 i 

65 

673 

8oi5 

8080 

8144 

8209 

827 3 

8338 

8402 

8467 

853i 

83 9 5 

64 

674 

8660 

8724 

8789 

8853 

8918 

8982 

9046 

9111 

9173 

9239 

64 

676 

9304 

9368 

9432 

9497 

956 i 

9625 

9690 

9754 

9818 

9882 

64 

676 

9947 

••11 

•® 7 5 

•189 

•204 

•268 

•332 

•896 

•460 

•525 

64 

6 77 

83 o 589 

o653 

0717 

0781 

0845 

0909 

0973 

\o3~i 

1102 

1166 

64 

678 

I23 o 

1294 

i358 

1422 

i486 

i55o 

1614 

1678 

1742 

1806 

64 

679 

1870 

1984 

1998 

2062 

2 j 26 

2189 

2253 

2317 

238i 

2445 

64 

680 

832609 

2673 

2637 

2700 

2764 

2828 

2892 

2o56 

3020 

3o83 

64 

681 

3i47 

3211 

3275 

3338 

3402 

3466 

353o 

35 9 3 

3657 

3721 

64 

682 

3784 

3848 

3912 

3973 

4039 

4io3 

4166 

423o 

4294 

4357 

64 

683 

442i 

4484 

4348 

4611 

4675 

4739 

4802 

4866 

4929 

4993 

64 

684 

5o56 

5l20 

5x83 

5247 

5310 

53j3 

5437 

55oo 

5564 

5627 

63 

685 

5691 

5754 

5817 

588i 

5944 

6007 

6071 

6)34 

6197 

6261 

63 

686 

6324 

6387 

645 i 

6514 

6377 

6641 

6704 

6767 

683o 

6894 

63 

687 

6957 

7020 

7083 

7146 

7210 

7273 

7 336 

789 9 

7462 

7525 

63 

688 

7388 

7652 

77 l5 

7778 

7841 

7904 

7967 

8o3o 

8093 

8156 

63 

689 

8219 

8282 

8345 

8408 

8471 

8534 

8397 

8660 

872 3 

8786 

63 

690 

838849 

8912 

8975 

9038 

9101 

9164 

9”7 

9289 

9 352 

9 4i5 

63 

691 

9478 

9641 

9604 

9667 

9729 

9792 

9833 

9918 

9981 

••43 

63 

692 

840106 

0169 

0232 

0294 

o35j 

0420 

0482 

o545 

0608 

0671 

63 

1 693 

0733 

0796 

0859 

0921 

0984 

1046 

1109 

1172 

1234 

1297 

63 

1 694 

i35o 

1422 

1485 

1547 

1610 

1672 

1735 

1 797 

i860 

1922 

63 

! 896 

i 9 85l 

2047 

2110 

2172 

2235 

2297 

236o 

2422 

2484 

2547 

62 

* 696 

2609 

2672 

2734 

2796 

2859 

1921 

2 9 83 

3o46 

3108 

3170 

62 

697 

3233! 

3295 

3357 

3420 

3482 

3544 

3 606 

3669 

373 i 

3793 

62 

698 

3855 

3oi8 

3980 

4042 

4104 

4166 

4229 

4291 

4353 

44i 5 

61 

699 

4477 

4639 

4601 

4664 

4726 

4788 

485 o 

4912 

4974 

5o36 

63 

N, 

0 

1 

2 

3 

4 

5 1 

6 

7 

8 

9 

1) 

















































































12 A. TABLE OF LOGARITHMS FROM I TO 10,000. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 


too 

846098 

5i6o 

5222 

5284 

5346 

5408 

5470 

5532 

5594 

5656 

6*2 

1° i 

5 7 i 8 

5 7 8o 

5842 

5904 

5 q 66 

6028 

6090 

6 i 5 i 

6213 

6275 

62 

J02 

633 t 

6399 

6461 

6523 

6585 

6646 

6708 

6770 

6832 

6894 

62 

]o3 

6955 

7 01 7 

7079 

7141 

7202 

7264 

7326 

7388 

7449 

7511 

62 i 

jo4 

75 7 3 

7634 

7296 

7758 

7819 

7881 

7943 

8004 

8066 

812S 

62 j 

Jo5 

S189 

8261 

8312 

83-74 

8433 

8497 

8559 

8620 

8682 

8743 

62 

706 

88o5 

8866 

P928 

8989 

9 o 5 i 

9112 

9 J 74 

9235 

9297 

9358 

611 

7° r 

9419 

9481 

9342 

9604 

9666 

9726 

9788 

9849 

991 1 

997- 

61 

708 

85oo33 

0096 

oi56 

0217 

0279 

o34o 

0401 

0462 

0024 

o585 

61 

709 

0646 

0707 

0769 

o83o 

0891 

0962 

1014 

1076 

1136 

1197 

61 

710 

8512 5S 

1320 

1381 

1442 

i5o3 

1564 

1625 

1686 

1747 

1809 

61 

7" 

1870 

iq 3 i 

1992 

2 o 53 

2114 

21 7 5 

2236 

2297 

2358 

12419 

61 

712 

2480 

2641 

2602 

2663 

2724 

2 7 85 

2846 

2907 

2968 

3029 

61 

7 1 3 

3090 

3i5o 

3211 

3 2 "j 2 

3333 

3394 

3455 

3 di 6 

3077 

3637 

61 

7i4 

3698 

3769 

3820 

3881 

3g4i 

4002 

4 o 63 

4124 

4 i 85 

4245 

61 

7*5 

43o6 

436 7 

4428 

4488 

4549 

4610 

4670 

473 i 

4792 

4852 

61 

fi6 

4 qi 3 

4974 

5o34 

5095 

5156 

52i6 

5277 

5337 

53 9 8 

5459 

61 

717 

5519 

558o 

6640 

5701 

5 7 6 i 

5822 

5882 

5943 

6oo3 

6064 

61 

li8 

6124 

6185 

6245 

63o6 

6366 

6427 

6487 

6048 

6608 

6668 

60 

|i9 

6729 

6789 

685o 

6910 

6970 

7 o3i 

7091 

7152 

7212 

7272 

60 

[20 

85 7 332 

7 3 9 3 

7453 

7 513 

7^74 

7634 

7694 

7755 

78 i 5 

7875 

60 

72* 

7 9 35 

7993 

8o56 

8116 

8176 

8236 

8297 

8357 

8417 

8477 

60 

f 22 

853 7 

83 9 7 

865 7 

8718 

8778 

8838 

8898 

8 9 53 

9018 

9078 

60 

723 

9138 

9198 

9258 

9818 

9 3 79 

9439 

9499 

9559 

9619 

9679 

60 i 

724 

97 3 9 

9799 

9859 

99'8 

9978 

••38 

••98 

® 158 

•218 

•278 

60 1 

725 

86o338 

o 3 9 8 

0458 

o5i8 

o3 7 8 

0637 

0697 

0767 

0817 

0877 

60 1 

726 

og37 

0996 

io56 

1116 

1176 

1236 

1295 

1355 

i 4 i 5 

1475 

60 

727 

1534 

i5g4 

i 654 

17U 

1773 

1833 

i 8 9 3 

1952 

2012 

2072 

60 

728 

2131 

2191 

2251 

23 io 

23 7 0 

2480 

2489 

2049 

2608 

2668 

60 

729 

2728 

2787 

2847 

2906 

2966 

3 o 25 

3o85 

3144 

3204 

3263 

60 

i3o 

863323 

3382 

3442 

35oi 

356i 

362 o 

368o 

3780 

3799 

3858 

59 

731 

3917 

3977 

4o36 

4096 

4155 

4214 

4274 

4333 

4892 

4452 

59 

7 32 

4611 

45 7 o 

463o 

4689 

4748 

4808 

4867 

4926 

4986 

5 o 45 

59 

7 33 

5104 

5163 

5222 

5282 

5341 

5400 

5469 

5019 

5578 

5637 

5o 

734 

5696 

5 7 55 

5814 

58 7 4 

5 9 33 

5992 

6o5i 

6110 

6169 

6228 

5 9 

7 35 

6287 

6346 

64o5 

6465 

6524 

6583 

6642 

6701 

6760 

6819 

5 9 

?36 

68 7 8 

6q3~I 

6996 

7 o55 

7114 

7173 

7232 

^ 1 

735o 

7409 

3 9 

7 3 7 

74 6 7 

7526 

73 85 

7644 

7703 

7762 

7821 

7880 

7939 

7998 

5 9 

7 38 

8o56 

8115 

8 i 7 4 

8233 

8292 

835o 

8409 

8468 

8527 

8586 

5g 

7 3 9 

8644 

8 7 o 3 

8762 

8821 

8879 

8 9 38 

8997 

9086 

9 u 4 

9173 

D9 

740 

869232 

9290 

9349 

9408 

9466 

9525 

9584 

9642 

9701 

9760 

5 9 

74i 

9818 

9877 

99 33 

9994 

••53 

•in 

•170 

•228 

•287 

•345 

5o 

742 

870404 

0462 

o 52I 

0379 

o638 

0606 

0755 

o8i3 

0872 

0930 

58 

743 

0989 

1047 

1 io6 

1164 

1223 

1281 

i 339 

i 3 9 8 

1456 

I3l5 

58 

744 

1573 

1631 

1690 

1748 

1806 

1865 

1923 

1981 

2040 

2098 

58 

745 

2156 

2 215 

22 7 3 

233 i 

2389 

2448 

2 Do 6 

2564 

2622 

2681 

58 

746 

2739 

2797 

2855 

2913 

2972 

3o3o 

3o88 

3146 

3204 

3262 

58 

747 

3321 

33 7 9 

343 7 

3495 

3553 

36i 1 

3669 

2727 

3785 

3844 

58 

748 

3902 

3960 

4018 

4076 

4134 

4192 

425o 

43o8 

4366 

4424 

58 

749 

4482 

4640 

4598 

4656 

4714 

4772 

483o 

4888 

4y45 

5oo3 

58 

7 5 o 

8 7 5o6i 

5i 19 

5*77 

5235 

5293 

535i 

5409 

5466 

5524 

5582 

58 

731 

564o 

5698 

5j56 

5813 

58 7 i 

5929 

5987 

6o45 

6102 

6160 

58 

7 D2 

6218 

6276 

6333 

6391 

6449 

6507 

6564 

6622 

6680 

6737 

58 

7 53 

6795 

6853 

6910 

6968 

7026 

70S3 

7141 

7199 

7256 

7 314 

58 

754 

7371 

7429 

7487 

7544 

7602 

765 9 

7717 

7774 

7832 

7889 

58 

733 

7947 

8004 

8062 

8119 

8177 

8234 

8292 

8349 

8407 

8464 

57 

7 56 

8522 8579 

863 7 

8694 

8 7 52 

8809 

8866 

8924 

8981 

90 J 9 

87 

7^7 

9096 

9i53 

9211 

9268 

9 323 

9383 

9440 

9l97 

9555 

9612 

57 

758 

9669 1 9726 

9784 

9841 

9898 

9986 

•®i 3 

••70 

•127 

®i85 

>7 

7^9 

880242 

0299 

o356 

04x3 

0471 

0628 

o585 

0642 

0699 

0766 

37 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 



































































A TABLE OF LOGARITHMS FROM 1 TO 10,000, 


18 


N. 

O 

1 

2 

3 

1 r~ 

1 4 

! 5 

j . 

6 

7 

8 

9 

D. 

760 

88081 ' 

l 0871 

0928 

og85 

1042 

1099 

1156 

1213 

1271 

i328 

57 

761 

j 38: 

1442 

1499 

1556 

1613 

1670 

1727 

1784 

1841 

1898 

67 

762 

195; 

2012 

2069 

2126 

2i83 

2240 

2297 

2354 

2411 

2468 

5 7 

76J 

252: 

258i 

2638 

2695 

2752 

2809 

2866 

2923 

2980 

3o37 

5y 

764 

309,' 

3i5o 

3207 

3264 

3321 

3377 

8434 

3491 

3 048 

36o5 

67 

76D 

3661 

3718 

3775 

3832 

3888 

3945 

4002 

4059 

4i 15 

4172 

57 

766 

422c 

4285 

4342 

4399 

4455 

4312 

4669 

4625 

4682 

4739 

67 

767 

479' 

4852 

4909 

4965 

5022 

6078 

5i 35 

5102 

5248 

53oo 

67 

768 

536i 

5418 

5474 

5531 

5587 

5644 

5700 

5 7 5 7 

5813 

5870 

5 7 

769 

592 6 

5 9 83 

6o3g 

6096 

61 52 

6209 

6265 

6321 

6378 

6434 

56 

770 

88649 1 

6547 

6604 

6660 

6716 

6773 

6829 

6885 

6942 

6998 

56 

; 771 

7004 

7111 

7167 

7223 

7280 

7336 

7392 

7449 

7600 

756i 

56 

772 

7617 

7674 

773o 

7786 

7842 

7898 

7933 

8011 

8067 

8123 

56 

773 

8x79 

8236 

8292 

8348 

8404 

8460 

85 6 

8673 

8629 

8685 

56 

774 

8741 

8797 

8853 

8909 

8965 

9021 

9°77 

9134 

9190 

9246 

56 

773 

9802 

9358 

9414 

947° 

9526 

9 582 

9 638 

9694 

9700 

9806 

56 

776 

9862 

9918 

9974 

®»3o 

••86 

•141 

®j 9 7 

•253 

•809 

•365 

56 

77 2 

890421 

0477 

o533 

o5§9 

0645 

0700 

0766 

0812 

0868 

0924 

56 

773 

0980 

io35 

1091 

H47 

1203 

1289 

1314 

1370 

1426 

1482 

56 

779 

1537 

1693 

1649 

I7o5 

1760 

1816 

1872 

1928 

1983 

2039 

56 

780 

892095 

2i5o 

2206 

2262 

2317 

237 3 

2429 

24S4 

2540 

25 9 5 

56 

781 

2651 

2707 

2762 

2818 

2373 

2929 

2 9 85 

3o4o 

3o 9 6 

3151 

56 

782 

3207 

3262 

3318 

33 7 3 

3429 

3484 

354o 

3595 

3651 

3706 

56 


3762 

3817 

38 7 3 

3928 

3984 

4o3 9 

4094 

4i5o 

42o5 

4261 

55 

784 

4316 

4371 

4427 

4482 

4538 

45 9 3 

4648 

4704 

47 5 9 

4814 

55 

785 

4870 

4925 

4980 

5o36 

5o 9 i 

6146 

5201 

5287 

5312 

5367 

55 

786 

5423 

5478 

5333 

5588 

5644 

5699 

5754 

5809 

5864 

5920 

55 

787 

5975 

6o3o 

6o85 

6140 

6i 9 5 

6231 

63o6 

6361 

6416 

6471 

55 

788 

6626 

6581 

6636 

6692 

6747 

6802 

6887 

6912 

6967 

7022 

55 

789 

7°77 

7132 

7187 

7242 

7297 

7352 

7407 

7462 

7517 

7 5 7 2 

55 

790 

897627 

7682 

7737 

7792 

7 847 

7902 

79 5 7 

8012 

8067 

8122 

55 

791 

8176 

8231 

8286 

8341 

83 9 6 

8451 

85o6 

8561 

8615 

8670 

55 

792 

8723 

8780 

8835 

8890 

8944 

8999 

9054 

9 :o 9 

9164 

9218 

55 

?9 3 

9273 

9328 

9 383 

9437 

9492 

9547 

9602 

9656 

9711 

9766 

55 

794 

9821 

9870 

9930 

9986 

••39 

®* 9 4 

•149 

•2o3 

•258 

•312 

55 

/ 9 d 

900367 

0422 

0476 

o53i 

o586 

0640 

o6 9 5 

0749 

0804 

0859 

55 

796 

0913 

0968 

1022 

1077 

1131 

1186 

1240 

I2 9 5 

1349 

1404 

55 

797 

1458 

1513 

1567 

1622 

1676 

1731 

1785 

1840 

1894 

1948 

54 

798 

2003 

2057 

2112 

2166 

2221 

2273 

2329 

2384 

2438 

2492 

54 

799 

2047 

2601 

2655 

2710 

2764 

2818 

2873 

2927 

2981 

3o36 

54 

Boo 

903090 

3144 

3199 

3253 

3307 

336x 

3416 

3470 

3524 

35 7 8 

54 

Bo 1 

3633 

368 7 

3741 

3795 

3849 

3904 

3 9 58 

4012 

4066 

4120 

54 

802 

4174 

4229 

4283 

4337 

4391 

4446 

4499 

4553 

4607 

4661 

54 

8o3 

4716 

4770 

4824 

4878 

4982 

4986 

5o4o 

5o 9 4 

5148 

5202 

54 

804 

5256 

5310 

5364 

5418 

5472 

5526 

558o 

5634 

5688 

5742 

54 

Bo5 

5796 

585o 

5904 

5958 

6012 

6066 

6119 

6173 

6227 

6281 

54 

806 

6335 

63 89 

6443 

6497 

655i 

66o4 

6658 

6712 

6766 

6820 

54 

8°7 

6874 

6927 

6981 

7 o36 

7089 

7143 

7196 

7260 

73o4 

7358 

54 

808 

7411 

7465 

7519 

757 3 

7626 

7680 

7734 

7787 

7841 

7895 

54 

809 

7949 

8002 

8o56 

8110 

8i63 

8217 

8270 

8324 

83 7 8 

843i 

54 

810 

508485 

853 9 

85 9 2 

8646 

8699 

8 7 53 

8807 

8860 

8914 

8967 

54 

811 

9021 

9074 

9128 

9181 

9235 

9289 

9342 

9396 

9449 

9 5o3 

54 

812 

9556 

9610 

9 663 

9716 

9770 

9828 

9877 

9930 

9984 

••37 

53 

8i3 { 

510091 

0144 

0197 

02DI 

o3o4 

o358 

0411 

0464 

o5i8 

0571 

53 

814 

0624 

0678 

0731 

0784 

o838 

0891 

0944 

0998 

io5i 

1104 

53 

8 1 5 

1158 

1211 

1264 

1317 

137 

1424 

1477 

i53o 

1584 

1637 

53 

816 

1690 

1743 

1797 

i85o 

1903 

1966 

2009 

2o63 

2116 

2169 

53 

817 

2222 

2275 

2328 

2381 

2435 

2488 

2541 

2594 

2647 

2700 

53 

818 

2753 

2806 

2859 

2 9 i3 

2966 

3oi 9 

3072 

3125 

3178 

3231 

53 

819 

3284 

3337 

3390 

3443 , 

3496 

3549 

36o2 

3655 

3708 

3761 

53 

k: 

0 

1 

2 

3 1 

4 ! 

5 

6 

7 

1 

8 

9 

D. 

























































































L4 A TABLE OF LOGARITHMS FROM I TO 10,000. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

820 

821 

822 

823 

824 
820 

826 

827 

828 

829 

830 

831 

832 

833 

834 

835 

836 

83 7 

838 

83 9 

840 

841 

842 

843 

844 

845 

846 

847 

848 

849 

850 

851 

852 

853 
864 

855 

856 

85 7 

858 

85 9 

860 

861 

862 

863 

864 

865 

866 

867 

868 

869 

870 

871 

872 

873 

874 

876 

876 

877 

878 

879 

9 i 38 i 4 

4343 

4872 

5400 

5927 

6454 

6980 

7D06 

8o3o 

8555 

919078 

9601 

920128 
0646 
1166 
1686 
2206 
2725 
3244 
3762 

924279 

4796 

53i2 

5828 

6342 

6857 

7370 

7883 

83 9 6 

8908 

929419 

9 9 3 o 

9 3 o 44 o 

0949 

1458 

1966 

2474 

2981 

3487 

3 99 3 

934498 
5oo3 
55o7 
6011 
6514 
7016 
7618 
8019 
8520 
9020 

9395 9 

940018 

o5i6 

1014 

1511 

2008 

25 o 4 

3ooo 

34 9 5 

3989 

; 3867 
4396 
4925 

5453 

5980 
6507 
70 33 
7558 
8o83 
8607 

9 i 3 o 

9653 

0176 

0697 

1218 

1738 

2258 

2777 

3296 

3814 

4331 
4848 
5364 
5879 
63 9 4 
6908 
7422 
79 35 
8447 

8969 

9470 

9981 

0491 

1000 

15o 9 
2017 
2624 
3o3i 
3538 
4044 

4549 

5 o 54 

5558 

6061 

6564 

7066 

7568 

8069 

8670 

9070 

9 56 9 

0068 

o566 

1064 

i56i 

2o58 

2554 

3 o 49 

3544 

4 o 38 

3 9 2 o 

4449 
4977 
55o5 
6o33 
655 9 
7085 
7611 

8135 
865g 

9183 

9706 

0228 

0749 

1270 

1790 

23lO 

2829 

3348 

3865 

4383 

4899 

54 io 

5 9 3 i 

6445 

6g5g 

7473 

7986 

8498 

9010 

9 521 

••32 

o 542 

io 5 i 

i56o 

2068 

2576 

3o82 

3589 

4094 

4599 

5104 
56o8 

6111 

6614 

7117 

7618 
811 9 
8620 
9120 

9619 

0118 

0616 

1114 

1611 
2107 

26o3 

3099 

35 9 3 

4088 

3973 

4302 

5o3o 

5558 

6o85 

6612 

7138 
7663 
8188 
8712 

9235 

9?58 

0280 

0801 

1322 

1842 

2362 

2881 

3399 

3917 

4434 

4951 

5467 

5982 

6497 

7011 

7524 

8037 

8549 

9061 

9 5 7 2 

••83 

0592 

I 102 
l6lO 
2Il8 

2626 

3133 
3639 
4145 

465o 

5154 
5658 
6162 
6665 
7167 

7668 

8169 

8670 

9170 

9669 

0168 

0666 

1163 
1660 
2157 
2653 
3 i 48 
3643 
4i37 

4026 
4555 
5o83 
5611 

6138 

6664 

7190 

77*6 

8240 

8764 

9287 
9810 
o 332 
oS53 
1374 
1894 
24U 
2933 
3451 
3969 

4486 
5oo3 
5518 
6o34 
6548 
7062 

tit 

8601 

9112 

9623 
• 134 
0643 

1153 
1661 
2169 
2677 

3183 
3690 
4195 

4700 

52 o 5 

5709 

6212 

6715 

7217 

77 1 8 
8219 
8720 
9220 

9719 

0218 

0716 

1213 
1710 
2207 
2702 

3198 
36g2 
4186 

4070 

4608 

5136 
5664 
6191 
6717 
7243 
7^8 
8293 

8816 

9840 

9862 

o3S4 

0906 
1426 
; 946 
2466 
2 9 85 
35o3 
4021 

4538 

5o54 

5570 

6o85 

6600 

7114 

7627 

8140 

8652 

9 i 63 

9674 
• 185 
0694 
1204 
1712 
2220 
2727 
3234 
3740 
4246 

475 i 

5255 

5 7 5 9 

6262 

6765 

7267 

7769 

8269 

8770 

9270 

9769 

0267 

0765 

1263 

1760 

2256 

2752 

3247 

3742 

4236 

4 i 32 

4660 

6189 

5716 

6243 

6770 

7295 

7820 

8345 

8869 

9392 

99*4 

0436 

0958 

1478 

1998 
2D I 8 

3o3-j 

3555 

4072 

4589 

5106 
5621 
6137 
6651 
7i65 
7678 
9191 
8703 
9215 

9725 

•236 

0745 

1254 

1763 

2271 

2778 

3285 

3791 

4296 

4801 
53o6 
5809 
6313 
6815 
73 i 7 
7819 
8320 
8820 
0320 

9819 
o3i7 
0815 

1313 
1809 
23 o 6 
2801 
3297 
379 1 
4285 

4184 
47 «3 
5241 
6769 
6296 
6822 
7348 
7873 
8397 
8921 

9444 

9967 

0489 

1010 

i53o 

2o5o 

2670 

3o8 9 

3607 

4124 

4641 

515 7 
5673 
6188 
6702 
7216 
773o 

8242 

8754 

9266 

977 6 

•287 

0796 

i3o5 

1814 

2322 

2829 

333 d 

3841 

4347 

4852 

5356 

586o 

6363 

6865 

7367 

i860 

8370 

O870 

9369 

9869 

0367 

o865 

1362 
i85g 
235 d 
285 i 
3346 
3841 
4335 

4237 

4766 

5294 

5822 

6349 

6875 

74oo 

7925 

845o 

8973 

9496 

••19 

o 54 i 

1062 

1582 
2102 
2622 

3140 
3658 
4176 

4693 

5209 

5725 

6240 

6754 

7268 

7781 

8293 

88o5 

9317 

9827 

•338 

0847 

1356 

1865 
2372 

2879 

3386 

3892 

4397 

4902 

5406 

5 9 io 

6413 

6916 

74i8 

79*9 

8420 

8920 

9419 

9918 

0417 

0915 
1412 

1909 

24o5 

2901 

3396 

38 9 o 

4384 

4290 

4819 

5347 

5875 

6401 

6927 

7453 

9026 

9549 

••71 

o 5 9 3 
:u4 
1634 
2154 
2674 
3 i 9 2 
3710 
4228 

4744 

5261 

5776 

6291 

68o5 

7 3i 9 

7 83 2 

8345 

885i 

9 368 

9879 

•38 9 

0898 

1407 

1915 

2423 

2 9 3 o 

3437 

J943 

4448 

4 9 53 

5457 

5960 

6463 

6966 

7468 

7969 

8470 

8970 

9469 

9968 

0467 

0964 

1462 

1968 

2455 

2 9 5 o 

3445 

3939 

4433 

53 

53 

53 

53 

53 

53 

53 

52 

5a 

5a 

52 

52 

52 

5a 

52 

5a 

52 

5a 

5 a 
52 

52 

52 

5a 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5i 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5o 

5 9 

Dg 

5 9 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 1 

D. 














































































15 


A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

0 

I 

2 

3 

4 

1 5 

1 

6 

7 

8 

9 

D. 

88o 

944483 

4532 

458i 

4631 

4680 

4729 

4779 

4828 

4877 

4927 

49 

831 

4976 

5o25 

6074 

5124 

6173 

52 2 2 

6272 

5321 

5370 

5419 

49 

882 

5469 

5518 

5567 

5616 

5665 

57l5 

5764 

5813 

5862 

5912 

49 

883 

6961 

6010 

6009 

6108 

6167 

6207 

6256 

63o5 

6354 

6403 

49I 

884 

64D2 

65oi 

6551 

6600 

6649 

6698 

6747 

6796 

6845 

6894 

49 

885 

6943 

6992 

7041 

7090 

7140 

7189 

7238 

7287 

7336 

7385 

49 

886 

7434 

7483 

7532 

i 5 Si 

763o 

7679 

7728 

7777 

7826 

7875 

49 

887 

7924 

7973 

8022 

8070 

8119 

8l68 

8217 

8266 

8315 

8364 

49 

883 

84i3 

8462 

8511 

856o 

8609 

8657 

8706 

8755 

8804 

8853 

49 

889 

8902 

8961 

8999 

9048 

9097 

9146 

9195 

9244 

9292 

9341 

49 

890 

949390 

9439 

9488 

953o 

g585 

9634 

9683 

973i 

9780 

9829 

49 

891 

^9878 

9926 

9975 

••24 

••73 

•121 

•170 

•219 

•267 

•316 

49 

892 

95o365 

0414 

0462 

o5i 1 

o56o 

0608 

0667 

0706 

0754 

o8o3 

49 

8 9 3 

o35i 

0900 

0949 

°997 

1046 

1095 

1143 

1192 

1240 

1289 

49 

894 

1338 

1386 

1435 

1483 

1532 

i58o 

1629 

i6 77 

1726 

1770 

49 

896 

1823 

1872 

IQ20 

1969 

2017 

2066 

2114 

2i63 

2211 

2260 

48 

896 

23o8 

2356 

2406 

2453 

2502 

255o 

2599 

2647 

2696 

2744 

48 

897 

2792 

2841 

2889 

2938 

2986 

3o34 

3o83 

3131 

3180 

3228 

48 

898 

3276 

3325 

3373 

342i 

3470 

3518 

3566 

36i5 

3663 

3711 

48 

899 

3760 

38o8 

3856 

3905 

3 9 53 

4001 

4049 

4098 

4146 

4194 

48 

900 

954243 

4291 

4339 

4387 

4435 

4484 

4532 

458o 

4628 

4677 

48 

901 

4720 

4773 

4821 

4B6g 

4918 

4966 

5oi4 

5o62 

5i 10 

5i58 

48 

902 

5207 

5255 

53o3 

5351 

5899 

5447 

5495 

5543 

5592 

5640 

48 

903 

5688 

5736 

5784 

583 2 

588o 

5928 

5976 

6024 

6072 

6120 

48 

904 

6168 

6216 

6265 

6313 

6361 

6409 

6407 

65o5 

6553 

6601 

48 

oo5 

6649 

6697 

6745 

6793 

6840 

6888 

6936 

6984 

7032 

7080 

48 

906 

7128 

7176 

7224 

7272 

7320 

7 36S 

7416 

7464 

7512 

7559 

48 

907 

7607 

7655 

77°3 

775i 

7799 

7 8 47 

7894 

7942 

7999 

6o38 

48 

908 

8086 

8134 

8181 

8229 

8277 

8325 

8373 

8421 

8468 

85i6 

48 

9°9 

8564 

8612 

8669 

8707 

8755 

88o3 

885o 

8898 

8946 

8994 

48 

QIO 

969041 

9089 

9 ,3 7 

9185 

9232 

9280 

9328 

9 3 75 

9423 

947 1 

48 

9' 1 

9618 

9666 

9614 

9661 

9709 

9757 

9804 

9852 

9900 

9947 

48 

912 

9996 

••42 

••90 

• 138 

• 185 

•233 

•280 

•328 

•076 

•423 

48 

9 i3 

960471 

o5i8 

o566 

o6i3 

0661 

0709 

0756 

0804 

o85i 

0899 

48 

914 

0946 

0994 

1041 

1089 

1136 

1184 

I 231 

1270 

i326 

1374 

47 

9 i5 

1421 

1469 

1516 

1563 

1611 

1658 

1706 

1753 

1801 

1848 

47 

oi6 

1896 

1943 

1990 

2o38 

2o85 

213 2 

2180 

2227 

2275 

232-2 

47 

917 

236o 

2417 

2464 

2511 

2559 

2606 

2653 

2701 

2748 

2 79 5 

47 

918 

2843 

2890 

2937 

2985 

3o32 

3079 

3i26 

3i74 

3221 

3268 

47 

9 1 9 

33i6 

3363 

34io 

3457 

35o4 

3552 

8699 

3646 

3698 

3741 

47 

920 

963788 

3835 

3882 

3929 

3 977 

4024 

4071 

4118 

4i65 

4212 

47 

921 

4260 

4307 

4354 

4401 

4448 

449 5 

4542 

4590 

4637 

4684 

47 

922 

4731 

4778 

4826 

4872 

4919 

4966 

5oi3 

5o6i 

5108 

5155 

47 

9 23 

5202 

5249 

6296 

5343 

5390 

5437 

6484 

5531 

5578 

5625 

47 

924 

5672 

5719 

5766 

5813 

586o 

5907 

5954 

6001 

6048 

6095 

47 

92D 

6l42 

6189 

6236 

6283 

6329 

6376 

6423 

6470 

65i 7 

6564 

47 

926 

66l 1 

6658 

6706 

6752 

6799 

6845 

6892 

6939 

6986 

7o33 

47 

III 

7080 

7127 

7 1 73 

7220 

7267 

7314 

736i 

74o8 

7454 

75oi 

47 

7648 

7093 

7642 

7688 

7735 

7782 

7829 

7875 

7922 

7969 

47 

929 

80l6 

8062 

8109 

8156 

8203 

8249 

8296 

8343 

8390 

8436 

47 

93o 

968483 

853o 

8676 

8623 

8670 

8716 

8 7 63 

8810 

8856 

8903 

47 

981 

8960 

8996 

9043 

9090 

9136 

9i83 

9229 

9276 

9 3 23 

9369 

47 

932 

94l6 

9463 

q5o9 

9556 

9602 

9649 

9696 

9742 

9789 

9830 

47 

933 

9882 

9928 

9976 

••21 

••68 

•114 

• 161 

•207 

•264 

•3oo 

47 

934 

970347 

0393 

0440 

0486 

o533 

o5 79 

0626 

0672 

°7>9 

0766 

40 

o35 

08l2 

0808 

0904 

0961 

°997 

1044 

1090 

1137 

11 S3 

1229 

46 

9 36 

1276 

13 2 2 

1069 

1415 

1461 

i5oS 

1554 

1601 

1647 

1693 

46 

937 

1740 

1786 

183 2 

1879 

1925 

1971 

2018 

2064 

2110 

2107 

46 

o38 

2203 

2249 

2296 

2342 

2383 

2434 

2481 

2627 

2673 

2619 

46 

939 

2666 

2712 

2738 

2804 

285 i 

2897 

2943 

2989 

3o3> 

3o82 

46 

N, 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

— 


25 




































































16 A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 


N. 

0 

1 

» 

2 

3 

4 

5 

6 

7 

8 

9 

H. 

940 

973128 

3i74 

3220 

3266 

3313 

335g 

34o5 

3451 

3497 

3543 

46 

941 

3590 

3636 

3682 

3728 

3774 

3820 

3866 

3 9 i 3 

3 9 5 9 

4 oo 5 

46 

| 942 

4 g 5 i 

4097 

4 > 43 

4189 

4235 

4281 

4827 

4374 

4420 

4466 

46 

943 

45i2 

4538 

1 4604 

465 o 

4696 

4742 

4788 

4834 

4880 

4926 

46 

944 

4972 

5oi8 

3064 

5 i 10 

5156 

5202 

0248 

5294 

5340 

5J86 

46 

945 

5432 

5478 

5524 

5570 

56i6 

5662 

5707 

5 7 53 

5799 

5845 

46 

946 

5891 

6937 

5 9 83 

6029 

6075 

6121 

6167 

6212 

6258 

63oi 

46 

947 

635o 

63 9 6 

6442 

6488 

6533 

6579 

6625 

6671 

6717 

6 7 63 

46 

948 

6808 

6854 

6900 

6946 

6992 

7037 

7083 

7129 

7170 

7220 

46 

949 

7266 

7312 

7358 

74o3 

7449 

7495 

7541 

7586 

7632 

7678 

46 

95 o 

977724 

7769 

7815 

7861 

7906 

7 9 52 

7298 

8043 

8089 

8135 

46 

951 

8181 

8226 

8272 

8317 

8363 

8409 

8454 

85oo 

8546 

85 9 i 

46 

952 

8637 

8683 

8728 

8774 

881 g 

8865 

8911 

8 9 56 

9002 

9047 

46 

953 

9093 

9138 

9184 

9230 

9275 

9321 

9366 

9412 

9457 

9 5 o 3 

46 

954 

9548 

9394 

9639 

9 685 

9730 

9776 

9821 

9867 

99 12 

99 58 

46 

955 

980003 

0049 

0094 

0140 

oi85 

023 I 

0276 

0322 

0367 

0412 

45 

956 

0458 

o5o3 

0649 

0594 

0640 

o685 

0730 

0776 

0821 

0867 

45 

957 

0912 

0967 

ioo3 

1048 

1093 

1139 

1184 

1229 

1275 

1320 

45 

958 

1366 

1411 

1456 

i 5 oi 

1547 

1692 

1687 

i683 

1728 

1773 

45 

959 

1819 

1864 

I 9°9 

1954 

2000 

2040 

2090 

2135 

2181 

2226 

45 

960 

982271 

23 i 6 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

45 

961 

2723 

2769 

2814 

2859 

2904 

2949 

299 i 

3 040 

3o85 

3i3o 

45 

962 

3176 

3220 

3265 

33io 

3356 

3401 

3446 

3491 

3536 

3581 

45 

963 

3626 

3671 

3716 

3762 

3807 

3852 

3«97 

3942 

3987 

4 o 32 

45 

964 

4077 

4122 

4167 

4212 

4257 

43 o 2 

4347 

4392 

4437 

4482 

45 

965 

4527 

4572 

4617 

4662 

4707 

4762 

4797 

4842 

4887 

4 9 32 

45 

966 

4977 

5o2 2 

6067 

5i 12 

5157 

5202 

5277 

6292 

5337 

5382 

45 

967 

5426 

5471 

5516 

556i 

56o6 

5651 

6696 

5 7 4i 

6786 

583o 

45 

968 

6875 

5920 

5965 

6010 

6o55 

6100 

6144 

6189 

6234 

6279 

45 

969 

6324 

6869 

64 i 3 

6458 

65o3 

6548 

6593 

663 7 

6682 

6727 

45 

970 

986772 

6817 

6861 

6906 

6 q 5 i 

6996 

7040 

7085 

7i3o 

7 J 7 5 

45 

97i 

7219 

7264 

7 3°9 

7 353 

739§ 

7443 

7488 

7532 

7577 

7622 

45 

972 

7666 

7711 

7756 

7800 

7840 

7800 

7934 

7979 

8024 

8068 

45 

973 

8113 

8l57 

8202 

8247 

8291 

8336 

8381 

842! 

8470 

8514 

45 

974 

8559 

86o4 

8648 

8693 

8737 

8782 

8826 

8871 

8916 

8960 

45 

973 

9003 

9049 

9094 

9138 

9183 

9227 

9272 

9 316 

9 361 

9 4 o 5 

45 

976 

q 45 o 

9494 

9 53 ? 

9 583 

9628 

9672 

97 1 7 

9761 

9806 

9 85 o 

44 

977 

978 

9895 

99 o 33 q 

9930 

0383 

9983 

0428 

co 2 8 

0472 

**72 

o5i6 

*117 

o56i 

°i6i 

o6o5 

•206 

o65o 

•25 o 

0694 

•294 

0738 

44 

44 

979 

0788 

0827 

0871 

0916 

0960 

1004 

1049 

io 9 3 

1137 

1182 

44 

9S0 

991226 

1270 

1315 

1359 

i4o3 

1448 

1492 

1536 

M 

O0 

O 

1625 

44 

981 

1669 

1713 

1758 

1802 

1846 

1890 

1935 

*979 

2023 

2067 

44 

982 

2111 

2156 

2200 

2244 

2288 

2333 

2377 

2421 

2465 

25 o 9 

44 

983 

2554 

25 9 8 

2642 

2686 

2730 

2 774 

2819 

2863 

2907 

2 9 5 i 

44 

984 

2 99 5 

3o4 9 

3o83 

3127 

3172 

32i6 

3260 

33o4 

3348 

33 9 2 

44 

985 

3436 

3480 

3524 

3568 

3613 

3657 

3701 

3745 

3789 

3833 

44 

986 

38 77 

3 o 2I 

3966 

4009 

4 o 53 

4097 

4141 

4i 85 

4229 

4273 

44 

987 

43i7 

4361 

44 o 5 

4449 

449 3 

4537 

4581 

4625 

4669 

4713 

44 

988 

4757 

4801 

4845 

4889 

4933 

4977 

5021 

5o65 

5108 

5152 

44 

989 

5196 

5240 

5284 

5328 

5372 

5 4 i 6 

5460 

55 o 4 

5547 

55 9 i 

44 

990 

995635 

56 79 

5723 

5767 

58n 

5854 

58g8 

5 9 42 

5 9 86 

6o3o 

44 

991 

6074 

6117 

6161 

62o5 

6249 

6293 

6337 

638o 

6424 

6468 

44 

992 

65i2 

6555 

6599 

6643 

6687 

6731 

6774 

6818 

6862 

6906 

44 

99 3 

6949 

6993 

7037 

7080 

7124 

7168 

7212 

7255 

7209 

7343 

44 

994 

7386 

743o 

7807 

7474 

7017 

756 i 

76o5 

7648 

7692 

7736 

7779 

44 

993 

7823 

79 10 

7954 

7998 

8041 

8o85 

8129 

8172 

8216 

44 

996 

8269 

83 o 3 

8347 

8390 

8434 

8477 

8521 

8564 

8608 

8652 

44 

997 

86 9 5 

8 7 3 9 

8782 

8826 

8869 

8913 

8 9 56 

9000 

9043 

9087 

44 

998 

9131 

9H4 

9218 

9261 

9 3o5 

9348 

9 3 9 2 

9435 

9479 

9 522 

44 

999 

9565 

9609 

9652 

9696 

9739 

9783 

9826 

9870 

99 l3 

99 5 7 

43 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 ). 






















































































A TABLE 


OF 

LOGARITHMIC 

SINES AND TANGENTS 

FOR EVERY 

DEGREE AND MINUTE 

OF THE QUADRANT. 


Remark. The minutes in the left-hand column of eacto 
page, increasing downwards, belong to the degrees at the 
top; and those increasing upwards, in the right-hand column, 
belong to the degrees below. 



18 (0 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

IX 

Cotang. 


0 



10-000000 


0•000000 


Infinite. 

60 

i 

6-463726 

5017-17 

000000 

• 00 

6-463726 

5017-17 

i 3-536274 

5 <? 

2 

764756 

2934-85 

000000 

• 00 

764766 

2934-83 

235244 

58 

3 

940847 

2 o 82 - 3 i 

000000 

• 00 

940847 

2082- 3 i 

059153 

5 ? 

4 

7-066786 

161 5 •17 

000030 

• 00 

7-066786 

161 5 -17 

12-934214 

56 

£ 

162696 

1 3 19•68 

000000 

• 00 

162696 

1 3 19•69 

831304 

55 

t 

241877 

1110-70 

9-999999 

• 01 

241878 

1110-78 

758122 

54 

7 

308824 

066-53 

999999 

• 01 

3 o 8825 

996 ■53 

691175 

53 

8 

3668 16 

852-54 

999999 

• 01 

366817 

852-54 

633 1 83 

52 

9 

4 17968 

762-63 

999999 

•01 

41797 ° 

762-63 

582 o 3 o 

5 i 

10 

463726 

689-88 

999998 

*01 

463727 

689-88 

536273 

5 o 

11 

7• 5 o 5 i18 

629-81 

9-999998 

• 01 

7»5o5i2o 

629-81 

12-494880 

49 

12 

542906 

679 .36 

999997 

• 01 

542909 

579-33 

407091 

48 

i 3 

577668 

536-41 

999997 

• 01 

577672 

536-42 

422328 

47 

14 

609853 

499-38 

999996 

-01 

609867 

499 • 3 9 

390143 

46 

i 5 

639816 

467-14 

999996 

• 01 

639820 

467-10 

36 oi 8 o 

45 

16 

667845 

438 - 8 i 

999995 

• 01 

667849 

438-82 

332 1 5 i 

44 

17 

694173 

4 1 3 •72 

999995 

• 01 

694179 

4 1 3 •73 

3o582i 

43 

A S 

7 i 8 997 

391-35 

999994 

• 01 

719004 

391 -36 

280997 

267016 

42 

•9 

742477 

371-27 

999993 

• 01 

742484 

3-71-28 

4 i 

20 

764764 

353 -i 5 

999993 

• 01 

764761 

35 i -36 

235239 

4 o 

:i 

22 

7 - 785943 
806146 

336-72 

321-76 

9-999992 
99999 1 

•01 

•01 

7-785961 
8061 55 

336-73 

321-76 

12-214049 

193840 

& 

23 

825461 

3 o 8 -oj 

99999 ° 

•01 

826460 

3 o 8 •06 

174640 

3 ] 

24 

843934 

295-47 

999989 

•02 

843944 

2 o 5 - 4 9 

1 56 o 56 

36 

25 

861662 

283-88 

999988 

•02 

861674 

283-90 

138326 

35 

26 

878696 

895085 

273-17 

999988 

•02 

878708 

273-18 

121292 

34 

27 

263•23 

999987 

999986 

• 02 

896099 

263-25 

104901 

33 

28 

910879 

253 -99 

• 02 

910804 

254 -oi 

089106 

32 

20 

926119 

245-38 

999986 

• 02 

926134 

245 - 4 o 

070866 

3 i 

3 o 

940842 

237-33 

999983 

• 02 

940868 

237-35 

069142 

3 o 

3 i 

7-955082 

229-80 

9.999982 

•02 

7 - 955 ioo 

229-81 

12•044900 

29 

32 

968870 

222-73 

999981 

•02 

968889 

982253 

222-75 

o 3 i 111 

28 

33 

982233 

216-08 

999980 

•02 

216-10 

017747 

27 

34 

995198 

209-81 

999979 

•02 

995219 

209-83 

004781 

26 

35 

36 

8-007787 

020021 

203-90 
198-31 

999977 

999976 

•02 

•02 

8-007809 

020045 

20L92 

198-33 

11-992191 

9799°5 

25 

24 

37 

031919 

193-02 

999975 

•02 

o 3 io 45 

io 3 -o 5 

968055 

23 

38 

043.601 

188-01 

999973 

•02 

043627 

188.o 3 

956473 

22 

3-9 

o 54 / 8 i 

1 83•25 

999972 

•02 

054809 

183-27 

945191 

21 

40 

065776 

178-72 

999971 

• 02 

o 658 o 6 

178-74 

934194 

20 

4 i 

8-076500 

174-41 

9-999969 

•02 

8-076531 

174-44 

11-923469 

>9 

42 

086965 

170-31 

999968 

• 02 

086997 

170-34 

9i3oo3 

l8 

43 

097183 

166• 3 o 

999966 

•02 

0972 1 7 

166-42 

002783 

802797 

883067 

n 

44 

107167 

162-60 

999964 

•o 3 

107202 

162-68 

16 

45 

116926 

159-08 

999963 

•o 3 

11 6 o 63 

1 5 g• 10 

i 5 

46 

126471 

1 55 - 66 

999961 

•o 3 

126010 

i 5 o -68 

873490 

14 

4 T 

1 358 10 

1 52•38 

999959 

999958 

•o 3 

1 3585 1 

162-41 

864149 

i 3 

48 

144953 

149-24 

•o 3 

144996 

149-27 

855 oo 4 

12 

49 

153907 

146-22 

9999 5 ° 

•o 3 

153962 

146-27 

846048 

11 

5 o 

162681 

143-33 

999954 

•o 3 

162727 

U 3-36 

837273 

10 

5 i 

3-171280 

140 -54 

9-999952 

•o 3 

8-171328 

140-57 

11-828672 

0 

52 

I 797 i 3 

137-86 

999950 

•o 3 

1 79763 
i 88 o 36 

■fr? 0 

i 35-32 

820267 

8 

53 

187985 

1 35 •79 

999948 

•o 3 

811964 
8 o 3»44 

7 

54 

196102 

i 32 - 8 o 

999946 

•o 3 

196156 

i 32-84 

6 

55 

204010 

i 3 o- 4 i 

999944 

•o 3 

204126 

i 3 o -44 

795874 

788047 

5 

56 

2;1 8 q 5 

128-10 

999942 

•04 

211953 

128-14 

4 

57 

219681 

12.5-87 

999940 

•04 

219641 

125-90 

780369 

77280O 

3 

58 

2271.34 

123-72 

999938 

• 04 

227196 

123-76 

2 

5 9 

234557 

121-64 

999936 

•04 

234621 

121-68 

765379 

1 

60 

24 i 855 

119-63 

999934 

•04 

241921 

119-67 

758079 

0 


Cosine 

D. 

Sine | 

Cotang. 

D. 

Tang. 

M. 


(89 DEGREES.) 















































SINES AND TANGENTS. (1 DEGREE.) 19 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

8 * 24 i 855 

119*63 

9*999934 

*04 

8*241921 

119 

67 

11*758079 

60 

i 

249033 

117*68 

999932 

• 04 

249102 

in 

72 

700898 

5 q 

2 

266094 

1 1 5 • 80 

999929 

• 04 

256 i 65 

1 15 

84 

743835 

58 

3 

263042 

113*98 

999927 

•04 

263 11 5 

114 

02 

736885 

5 ? 

4 

269881 

112*21 

999925 

• 04 

269956 

11 2 

25 

730044 

56 

5 

276614 

iio* 5 o 

999922 

• 04 

276691 

110 

54 

723309 

55 

5 

283243 

1 08 *83 

999920 

• 04 

283323 

108 

87 

716677 

54 

7 

289773 

107*21 

999918 

.04 

289866 

107 

26 

710144 

53 

8 

296207 

io 5*65 

999915 

• 04 

296292 

io 5 

70 

703708 

52 

9 

302546 

104*i 3 

Q 999 1 3 

•04 

302634 

104 

18 

697366 

5 i 

10 

308794 

102*66 

999910 

*04 

3o8884 

102 

70 

691116 

5 o 

ii 

8• 3 14904 

101*22 

9.999907 

• 04 

8• 3 15046 

101 

26 

11*684954 

49 

12 

321027 

99*82 

999905 

• 04 

321122 

99 

87 

678878 

48 

i 3 

327016 

98*47 

999002 

•04 

3271 14 

98 

5 i 

672886 

47 

14 

332924 

97.14 

999899 

*o 5 

333025 

97 

19 

666975 

46 

i 5 

338753 

9 5 * 86 

999897 

• o 5 

338856 

90 

90 

661144 

45 

16 

3445 o 4 

94*60 

999894 

• o 5 

344610 

94 

65 

655390 

44 

*7 

35 oi 8 i 

9 3 *38 

999891 

*o 5 

350289 

9 3 

43 

649711 

43 

18 

355783 

92*19 

999888 

• o 5 

350890 

92 

24 

644 io 5 

42 

19 

36 1 3 1 5 

91 *o 3 

999885 

• o 5 

36 i 43 o 

9 1 

08 

638570 

41 

20 

366777 

89*90 

999882 

*o 5 

366895 

89 

9 5 

633 1o 5 

40 

21 

8*372171 

88* 80 

9*999879 

• o 5 

8*372292 

88 

85 

1 1*627708 

3 9 

22 

877499 

87*72 

999876 

• o 5 

377622 

87 

77 

622378 

38 

23 

382762 

86*67 

999873 

• o 5 

382889 

86 

72 

617111 

37 

24 

387962 

85*64 

999870 

■ o 5 

388092 

85 

70 

611908 

36 

25 

393101 

84-64 

999867 

• o 5 

393234 

84 

70 

606766 

35 

26 

398179 

83*66 

999864 

• o 5 

3983 i 5 

83 

7 i 

6 oi 685 

34 

27 

403199 

82*71 

999861 

• o 5 

4 o 3338 

82 

76 

596662 

33 

28 

408161 

8 i *77 

999868 

*o 5 

4 o 83 o 4 

81 

82 

591696 

32 

29 

4 i 3 o 68 

80 *86 

999804 

*o 5 

41 3 21 3 

80 

9 « 

586787 

3 i 

3 o 

417919 

79.96 

999851 

• 06 

418068 

80 

02 

581932 

3 o 

3 1 

8*422717 

79*09 

9*999848 

• 06 

8*422869 

79 

14 

1 1 •57713 1 

20 

32 

427462 

78*23 

999844 

*06 

427618 

78 

3 o 

572382 

28 

33 

43 21 56 

77.40 

999841 

*06 

4323 1 5 

77 

45 

567685 

27 

34 

4368 oo 

76*57 

999838 

• 06 

436962 

76 

63 

563 o 38 

26 

35 

44 i 394 

75-77 

999834 

• 06 

441060 

7 3 

83 

558440 

25 

36 

446941 

74-99 

99983i 

• 06 

446110 

73 

o 5 

553890 

24 

3 7 

460440 

74-22 

999827 

*o6 

45 o 6 i 3 

74 

28 

549387 

23 

38 

464893 

73*46 

999823 

•06 

455070 

73 

52 

544930 

22 

39 

459301 

72*73 

999820 

• 06 

469481 

72 

79 

540019 

21 

40 

463665 

72*00 

999816 

•06 

463849 

72 

06 

536 i 5 i 

20 

41 

8*467985 

71*29 

0 *qqq8i2 

• 06 

8*468172 

7 i 

35 

11*531828 

IQ 

42 

472263 

70*60 

999809 

• 06 

472454 

70 

66 

527546 

l8 

43 

476498 

69.91 

999805 

• 06 

476693 


98 

523307 

17 

44 

480693 

69*24 

999801 

• 06 

480892 

69 

3 i 

519108 

l6 

45 

484848 

68*59 

999797 

.07 

486000 

68 

65 

5 i 495 o 

i 5 

46 

488963 

67*94 

999793 

•°7 

489170 

68 

01 

5 io 83 o 

14 

47 

493040 

67*31 

999790 

.07 

490260 

67 

38 

606750 

i 3 

48 

497078 

66*69 

999786 

.07 

497293 

66 

76 

502707 

12 

49 

5 oio 8 o 

66* 08 

999782 

.07 

501298 

66 

i 5 

498702 

11 

5 o 

5 o 5 o 45 

65*48 

999778 

.07 

605267 

65 

55 

494733 

10 

5 i 

8*508974 

64-89 

9-999774 

*07 

8*509200 

64 

96 

1 1 *490800 

Q 

52 

512867 

64 - 3 1 

999769 

*07 

5 1 3 o 9 8 

64 

n 9 

486902 

8 

53 

616726 

63*75 

999765 

*07 

516961 

63 

82 

483 o 39 

7 

54 

52 o 55 i 

63*19 

999761 

*07 

520790 

63 

26 

479210 

6 

55 

524343 

62*64 

999757 

*07 

524586 

62 

72 

475414 

5 

56 

528102 

62*11 

999753 

•07 

528349 

62 

l8 

47i 65 i 

4 

57 

53 i 828 

61 *58 

999748 

*07 

532 o 8 o 

61 

65 

467920 

3 

58 

535523 

61 *06 

999744 

*07 

535779 

61 

i 3 

464221 

2 

59 

539186 

60 *55 

999740 

*07 

539447 

60 

62 

46 o 553 

1 

60 

542819 

60*04 

999735 

• 07 

548084 

60 

12 

456916 

0 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang 



16 (88 DEGREES.) 












































20 


(2 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sino 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

8-542819 

60-04 

9-999735 

• 07 

8• 543 o 84 

6o-12 

11-456916 

60 

i 

546422 

59-55 

999731 

•07 

546691 

59-62 

453309 

5 o 

2 

549995 

69-06 

999726 

.07 

55o268 

59-14 

449732 

58 

3 

553539 

58-58 

999722 

• 08 

553817 

58-66 

446 i 83 

57 

4 

557054 

58 -n 

999717 

• 08 

557336 

58 -19 

442664 

56 

5 

56 o 54 o 

57-65 

999713 

.08 

660828 

57.73 

439172 

55 

6 

563999 

67-19 

999708 

• c8 

564291 

67-27 

430709 

54 

7 

667431 

56-74 

999704 

•08 

567727 

56-82 

432273 

53 

8 

670836 

56 - 3 o 

999699 

• 08 

571137 

56-38 

428863 

52 

9 

574214 

55-87 

999694 

• 08 

574520 

55-95 

425480 

5 i 

10 

677566 

55 • 44 

999689 

• 08 

577877 

55-52 

422123 

5 o 

ii 

8•580892 

55-02 

9 -ooq 685 

• 08 

8 - 58 i 2 o 8 

55 -io 

11-418792 

49 

12 

584193 

54 - 6 o 

999680 

• 08 

584514 

54-68 

4 l 54 o 6 

48 

i 3 

587469 

54 -19 

999675 

• 08 

587795 

64-27 

412205 

47 

14 

590721 

53.79 

999670 

.08 

591061 

53-87 

408949 

46 

i 5 

698948 

53-39 

999665 

.08 

594283 

53-47 

405717 

45 

16 

697162 

53 -oo 

999660 

• 08 

597492 

53 -o 8 

402 5 o 8 

44 

*7 

6 oo 332 

52 -6i 

999655 

• 08 

600677 

52-70 

899323 

43 

18 

603489 

52-23 

999650 

.08 

6 o 3839 

52-32 

896161 

42 

»9 

60662 3 

5 i *86 

999645 

.09 

606978 

5 i -94 

393022 

4 i 

20 

609734 

5 i 49 

999640 

• 09 

610094 

5 1 • 58 

389906 

4 o 

21 

8-612823 

5 i • 12 

9 • qqq 635 

• 09 

8-613189 

5 l -21 

11 - 3868 11 

3 o 

22 

615891 

60-76 

999629 

•«/ 

616262 

5 o -85 

383738 

38 

23 

618937 

5 o- 4 i 

999624 

*°9 

619313 

5 o- 5 o 

380687 

37 

24 

621962 

5 o-o 6 

999619 

•09 

622343 

5 o -15 

377657 

36 

25 

624965 

49-72 

999614 

•°9 

625352 

49-81 

374648 

35 

26 

627948 

49-38 

999608 

-09 

628340 

49-47 

371660 

34 

27 

63091 i 

4 o-o 4 

999603 

•09 

63 1 3 o 8 

49. j 3 

368692 

33 

28 

633854 

48-71 

999597 

.09 

634256 

48 • 80 

365744 

• 3 a 

29 

636776 

48-39 

999592 

.09 

637184 

48 • 48 

362816 

3 i 

3 o 

639680 

48-06 

999586 

•°9 

640093 

48-16 

359907 

3 o 

3 1 

8-642563 

47-75 

9-999581 

*°9 

8-642982 

47-84 

11-357018 

29 

32 

645428 

47*43 

999575 

.09 

645853 

47-53 

354147 

28 

33 

648274 

47-12 

999570 

•°9 

648704 

47-22 

351296 

27 

34 

65 1102 

46-82 

999564 

.09 

65 1537 

46-91 

348463 

26 

35 

653911 

46-52 

999558 

• 10 

654352 

46-61 

045648 

25 

35 

656702 

46-22 

999553 

• 10 

657149 

46- 3 1 

34285 i 

24 

37 

659475 

45.92 

999547 

• 10 

659928 

46-02 

340072 

23 

38 

66223 o 

45-63 

999541 

• 10 

662689 

45-73 

3373i 1 

22 

3 9 

664968 

45-35 

999535 

• 10 

665433 

45-44 

334567 

21 

4 o 

667689 

45 • 06 

999529 

• 10 

668160 

45-26 

33 i 84 o 

20 

4 i 

8-670393 

44-79 

9-999524 

•10 

8-670870 

44-88 

11 - 329 i 3 o 

IQ 

42 

673080 

44 - 5 i 

999518 

• 10 

673563 

44 -61 

326437 

l8 

43 

675751 

44-24 

999512 

• 10 

676239 

44*34 

323761 

17 

44 

678405 

43-97 

999506 

• 10 

678900 

44-17 

321100 

l6 

43 

681043 

43-70 

999500 

• 10 

681044 

43 -80 

3 i 8456 

i 5 

46 

683665 

43*44 

999493 

• 10 

684172 

43 • 54 

3 i 5828 

14 

47 

686272 

43 • 18 

999487 

• 10 

686784 

43-28 

3 i 3 oi 6 

i 3 

48 

688863 

42-92 

999481 

• 10 

689381 

43 • o 3 

810619 

12 

49 

691438 

42-67 

999475 

• 10 

691963 

42-77 

3 o 8 o 37 

11 

5 o 

693998 

42-42 

999469 

• 10 

694029 

42-62 

3 o 547 i 

:o 

5 i 

8■696543 

42-17 

9-999463 

• 11 

8-697081 

42-28 

11-302919 

q 

52 

699073 

4 i -92 

999456 

• 11 

699617 

42-o 3 

3 oo 383 

ft 

53 

701589 

41 -68 

99945 o 

• 11 

702139 

41-70 

291861 

7 

54 

704090 

4 i -44 

999443 

-11 

704646 

4 i -55 

290354 

6 

55 

706577 

4l -21 

999437 

• 11 

707140 

41 -32 

292860 

5 

55 

709049 

40-97 

999431 

• 11 

709618 

41 - 08 

200382 

4 

57 

711507 

40-74 

999424 

• 11 

712083 

40 -85 

287917 

3 

58 

713952 

4 o- 5 i 

999418 

• 11 

714534 

40-62 

285465 

2 

59 

716383 

40-29 

999411 

• 11 

716972 

40-40 

288028 

1 

60 

718800 

4o-o6 

999404 

• 11 

719896 

40-17 

280604 

0 


Cosme 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. 

- 


(87 DEGREES.) 
























































SINES AND TANGENTS (3 DEGREES., 21 


j m. 

Sine 

D. 

Cosine 

D. 

Tang. 

B. 

Cotang. 


i© 

8*718800 

4o*o6 

9•999404 

• 11 

8*719396 

40*17 

11*280604 

6© 

< 

721204 

39*84 

999898 

*11 

721806 

39.95 

278194 

69 f 

2 

72319s 

39-62 

999891 

•11 

724204 

39*74 

276796 

58 J 


72:1972 

89*41 

999364 

• u 

726588 

39*52 

273412 

67 ' 

4 

728337 

39* 19 

•9993 /8 

• >ia 

7289)9 

39* 3 o 

271041 

56 

5 

730688 

38*98 

*999371 

* 11 

7 3 1 3 17 

39*09 

268683 

55 ! 

•» 6 

733027 

38*77 

999364 

•12 

733663 

38*89 

266337 

54 j 

7 

735354 

38*57 

999357 

•12 

736996 

38*68 

264004 

53 

8 

737667 

38*36 

999350 

•12 

7 383 17 

38*48 

26 i 683 

5 a , 

9 

739969 

38 * 16 

999343 

•12 

740626 

38*27 

269374 

5 i i 

to 

742259 

87*96 

999336 

• 12 

742922 

33*07 

267078 

5 o i 

IS 

8*744536 

37*76 

9 * 9 Qq 32 Q 

• 12 

8*745207 

37*87 

la -254793 

49 ' 

12 

746802 

37*56 

999822 

• 12 

747479 

37*68 

252521 

48 

i 3 

749055 

37-87 

99 g 3 1 5 

•12 

749740 

37*49 

200260 

47 | 

*4 

75 1297 

07*17 

999808 

• 12 

751989 

37*29 

248oiI 

46 

a 5 

7535 s 8 

36*98 

999301 

*12 

754227 

37*10 

240773 

45 

16 

755747 

36*79 

999294 

• 12 

756453 

36*92 

243547 

44 j 

*7 

757955 

36 * 6 i 

999286 

•12 

758668 

36*73 

241332 

43 i 

as 

7601 5 t 

36*42 

999279 

•12 

760872 

36*55 

239128 

42 

'19 

762337 

36*24 

999272 

* 12 

768060 

36*36 

236 g 35 

4 i 

i 20 

764021 

S6*o6 

999265 

•12 

765246 

36 • 18 

234754 

40 

21 

8*766675 

35*88 

9*999257 

*12 

8*767417 

36 *oo 

11*232583 

89 j 

22 

768828 

35 * 7 © 

999 25 o 

• l 3 

769578 

35*83 

230422 

38 i 

a 3 

770970 

35*53 

999242 

•i 3 

771727 

35*65 

228273 

3 7 

24 

773 ioi 

35*35 

999235 

• a 3 

77 3866 

35*48 

226134 

36 j 

23 

770223 

35 *i 8 

999227 

• i 3 

776996 

35 * 3 i 

224005 

35 

26 

777333 

35 -el 

099220 

•a 3 

77 8 ii 4 

35 *i 4 

221886 

34 ; 

! 27 

779434 

34-84 

999212 

• i 3 

780222 

34-97 

219778 

33 | 

28 

* 78 i 524 

34-67 

999203 

•i 3 

782320 

34-00 

217680 

32 > 

29 

7836 o 5 

34 - 5 x 

999 1 97 

• i 3 

784408 

34-64 

215592 

3 i 

So 

7856 7 5 

34 - 3 i 

999189 

•i 3 

786486 

34-47 

2 i 35 i 4 

3 o | 

3 i 

8*787736 

34 -i 8 

9*qqqi8i 

*a 3 

8•788554 

34 - 3 i 

11*211446 

29 

S2 

789787 

34-02 

999174 

• i 3 

790618 

3 4 • 1 5 

209387 

28 

33 

791828 

33*86 

999166 

• i 3 

792662 

33.99 

207338 

27 

34 

793859 

33 * 7 © 

9 qqi 58 

• i 3 

794701 

33*83 

205299 

26 i 

S 5 

79588 a 

33*54 

999160 

• i 3 

796731 

33*68 

203269 

25 ] 

36 

797894 

33.39 

999142 

• i 3 

798752 

33*52 

201248 

24 ! 

h 

799897 

33*23 

999134 

• i 3 

800763 

33-37 

199287 

23 

38 

801892 

33 * 08 

999IE6 

• i 3 

802765 

33*22 

197235 

22 


803876 

32*93 

999!18 

*i 3 

804758 

33*07 

196242 

21 ! 

40 

8 o 5852 

32*78 

999 11© 

•i 3 

806742 

32*92 

193268 

20 

41 

8*807819 

32*63 

9 *Q 9 Ql 02 

• i 3 

8*808717 

82*78 

11•191283 

19 ! 

42 

809777 

32*49 

999094 

•14 

8 io 683 

32*62 

189317 

18 1 

43 

811726 

32*34 

999086 

•14 

812641 

32*48 

187359 

17 

44 

8 i 366 t 

32*10 

999077 

•14 

814589 

32*33 

186411 

16 

45 

815599 

32 *o 5 

999069 

*14 

816529 

82*19 

■i 8347 x 

i 5 

46 

817522 

3 i *91 

999061 

•14 

818461 

32 *o 5 

181669 

14 

47 

819436 

3 1 • 77 

999053 

•14 

820884 

3 i *91 

179616 

i 3 ; 

48 

821343 

3 1 *63 

999044 

•u 

822298 

3 i -77 

177702 

12 | 

49 

823240 

3 1 *49 

999036 

•14 

824205 

3 1 *63 

176795 

11 

5 o 

8 s 5 i 3 o 

3 i *35 

999027 

•14 

826103 

3 1 * 5 o 

i 7 38 97 

to 


8*827011 

3 l *22 

9*999019 

.14 

8*827992 

3 1 *36 

11*172008 

9 ! 

52 

828884 

3 i *08 

999010 

•U 

829874 

3 1 • 23 

170126 

8 

53 

880749 

3 o*o 5 

999002 

•14 

831748 

3 1 • 10 

168252 

7 : 

54 

832607 

3 o *82 

998993 

•14 

8336 1 3 

30*96 

1 663 87 

6 

55 

834456 

30*69 

998984 

•14 

8354 7 i 

3 o *83 

164529 

5 

56 

836297 

3 o *56 

998976 

• u 

83 7 32 i 

3 o* 7 o 

162679 

4 -j 

57 

838 i 3 o 

3 o *43 

998967 

*i 5 

889163 

80*67 

i 6 o 83 7 

3. 

58 

839966 

3 o* 3 o 

998958 

• i 5 

840998 

3 o *45 

159002 

2 

59 

841774 

3 o* 17 

998950 

•i 5 

842825 

3 o *32 

157175 

s j 

60 

843535 

3 o*oo 

998941 

• i 5 

844644 

3 o* 19 

156366 

® ; 

l 

■Cosine 

D. 

Sine 


Cotang. 1 

P. 

Tang. 

M. 

_i 


(86 DEGREES.^ 
















































22 


(4 DEGREES.) A TABLE OF LOGARITHM K? 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

8*843585 

3 o*o 5 

9*998941 

• i 5 

8*844644 

3 o* 19 

ii*i 55356 

60 { 

i 

845387 

29*02 

998982 

• id 

846455 

30*07 

i 53545 

59 

2 

8471 83 

29*00 

998923 

• i 5 

848260 

29*96 

1 5 1740 

58 

3 

848971 

29*67 

998914 

• i 5 

85 oo 57 

29*82 

149943 

57 

4 

850761 

29*55 

998900 

• i 5 

85 1846 

29*70 

148154 

56 

5 

852525 

29*43 

998896 

• i 5 

853628 

29*68 

146372 

55 

6 

854291 

29 * 3 i 

998887 

• id 

8554 o 3 

29*46 

144697 

54 

7 

806049 

29* 19 

998878 

• i 5 

867171 

29*35 

142829 

53 

8 

857801 

29*07 

998869 

•i 5 

858932 

29*23 

141068 

5 a 

9 

859546 

28*96 

998860 

• ID 

860686 

29*11 

169314 

Ol 

1C 

861283 

28*84 

998801 

• i 5 

862433 

29*00 

187667 

5 ° 

ii 

8 * 863 oi 4 

28*73 

9*998841 

• i 5 

8*864173 

28*88 

11•135827 

49 

12 

864738 

28*61 

998832 

• i 5 

860906 

28*77 

134094 

48 

i 3 

866455 

28 * 5 o 

998823 

• 16 

867632 

28-66 

132368 

47 

i 4 

8681 65 

28*39 

998813 

• 16 

86 9 35 1 

28*54 

130649 

46 

ID 

869868 

28*28 

998804 

• 16 

871064 

28*43 

128936 

45 

! 16 

871 565 

28*17 

998795 

* 16 

872770 

28*32 

127230 

44 

n 

8 7 3255 

28*06 

998785 

. 16 

874469 

28-21 

1 2553 j 

43 

18 

874938 

27*95 

908776 

• 16 

876162 

28*11 

123838 

42 

J 9 

876615 

27*86 

998766 

• 16 

877849 

28*00 

1221 5 i 

4 i 

20 

878285 

27*73 

998757 

• 16 

879529 

27*89 

120471 

4 o 

! 21 

8*879949 

27*63 

9*998747 

• 16 

8*881202 

27*70 

11*118798 

3 q 

1 22 

881607 

27*52 

998738 

• 16 

882869 

27*68 

117161 

38 

23 

883258 

27*42 

998728 

• 16 

88453 o 

27*58 

116470 

37 

24 

884903 

27 • 3 1 

998718 

• 16 

8861 85 

27*47 

ii 38 i 5 

36 

25 

886042 

27*21 

998708 

• 16 

887833 

27.37 

112167 

35 

26 

888174 

27*11 

998699 

• 16 

889476 

27*27 

1io 524 

34 

27 

889801 

27*00 

998689 

• 16 

891112 

27*17 

108888 

33 

28 

891421 

26*90 

998679 

•16 

892742 

27*07 

107258 

32 

29 

8 g 3 o 35 

26*80 

998669 

•17 

894366 

26*97 

io 5634 

3 i 

3 o 

894643 

26*70 

998659 

•n 

895984 

26*87 

104016 

3 o 

3 i 

8*896246 

26*60 

9*998649 

• 17 

8*897596 

26*77 

11•102404 

20 

32 

897842 

26 - 5 i 

998639 

•17 

899203 

26*67 

100797 

28 

33 

899432 

26*41 

998629 

•n 

900803 

26*58 

099197 

37 

34 

901017 

26 * 3 i 

998619 

•17 

902398 

26*48 

097602 

26 

35 

902696 

26*22 

998609 

•n 

903987 

26*38 

096013 

25 

36 

904169 

26*12 

998599 

*17 

906070 

26*29 

094430 

24 

37 

905736 

26 *o 3 

998589 

*17 

907147 

26*20 

092853 

23 

38 

907297 

25*93 

998078 

*17 

908719 

26*10 

091281 

22 

3 9 

908853 

25*84 

998668 

•n 

910286 

26*01 

08971 5 

21 

4 o 

910404 

25*75 

998558 

*17 

911846 

25*92 

088154 

20 

4i 

8*911949 

25*66 

9*998548 

•17 

8*913401 

25*83 

11 *086099 

IO 

42 

913488 

25*56 

998537 

•17 

914951 

25*74 

085049 

l8 

43 

9 l 5 o 22 

25*47 

998627 

•17 

916495 

25*65 

o 835 o 5 

*7 

44 

9 i 655 o 

25*38 

998516 

•18 

918064 

25*56 

081966 

l6 

45 

918073 

25*29 

998506 

•18 

919568 

25*47 

080482 

i 5 

46 

919691 

25*20 

998495 

•18 

921096 

25*38 

078004 

14 

47 

921103 

25*12 

998485 

•18 

922619 

25 * 3 o 

077681 

i3 

48 

922610 

25 *o 3 

998474 

•18 

924i36 

25*21 

0-76864 

12 

49 

924112 

24*94 

998464 

•18 

926649 

25*12 

074351 

11 

5 o 

926609 

24*86 

998453 

•18 

927156 

25 *o 3 

072844 

10 

5 i 

8*927100 

24*77 

9 • 998442 

• 18 

8.928658 

24 *o 5 

11 071342 

9 

02 

928587 

24*69 

998431 

• 18 

93 oi 55 

24*86 

069845 

8 ! 

53 

930068 

24*60 

998421 

• 18 

931647 

24*78 

068353 

7 

54 

931544 

24*52 

998410 

• 18 

933i34 

24*70 

066866 

6 

55 

933 oi 5 

24*43 

998399 

• 18 

934616 

24*61 

o 65384 

5 

56 

934481 

24*35 

998388 

• 18 

986093 

24*53 

063(707 

4 

h 

935942 

24*27 

998377 

• 18 

937665 

24*45 

062436 

3 

58 

937398 

24*19 

998366 

• 18 

939032 

24*37 

060968 

2 


93885 o 

24*11 

998355 

•18 

940494 

24 * 3 o 

o 5 o 5 o 6 

1 


940296 

24*o3 

998344 

•18 

941902 

24*21 

o 58 o 48 

a 

! Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. 


(85 DEGREES.) 














































SINES AND TANGENTS. (5 DEGREE.) 


n 


M. 

Sine 

D. 

Cosine 

D. 

Tung. 

D. 

Cotang. 

o 

8-940296 

24-o3 

9-998344 

.19 

8-941952 

24 

21 

11•o58o48 

60 

i 

941708 

23.94 

998333 

.19 

943404 

24 

i3 

066596 

5c 

2 

943174 

23-87. 

998322 

-19 

944852 

24 

o5 

o55i48 

58 

3 

944606 

23.79 

998311 

.19 

946295 

23 

97 

o537o5 

57 

4 

946034 

23-71 

998300 

• 19 

947734 

23 

9° 

o52266 

56 

5 

947456 

23-63 

998289 

.19 

949168 

23 

82 

o5o832 

55 

6 

948874 

23-55 

998277 

•19 

950697 

23 

"4 

049403 

54 

7 

950287 

23-48 

998266 

-19 

952021 

23 

66 

047979 

53 

8 

951696 

23-4o 

998255 

-19 

953441 

23 

60 

046559 

52 

9 

953100 

23-32 

998243 

-19 

954856 

23 

5i 

o45i44 

5i 

10 

954499 

23-25 

998232 

• 19 

966267 

23 

44 

043733 

5o 

U 

8-9558o4 

23-17 

0*098220 

•*9 

8-957674 

23 

3 7 

11-042326 

49 

12 

957284 

23-10 

998209 

.19 

969075 

23 

2 9 

040925 

48 

i3 

958670 

23-02 

998107 

.19 

960473 

23 

23 

039527 

47 

14 

960052 

22-95 

998186 

-19 

961866 

23 

14 

o38i34 

46 

i5 

961429 

22-88 

998174 

.19 

963255 

23 

07 

036745 

45 

16 

962801 

22-80 

998168 

.19 

964639 

23 

00 

o3536i 

44 

*7 

964170 

22-73 

998 i 5 i 

.19 

966019 

22 

9 3 

033981 

43 

18 

965534 

22-66 

998139 

• 20 

967894 

22 

86 

032606 

42 

i 9 

966893 

22-59 

998128 

• 20 

968766 

22 

79 

o3i234 

4i 

So 

968249 

22-52 

998116 

•20 

970133 

22 

71 

029867 

40 

21 

8•969600 

22-44 

9-908104 

• 20 

8-971496 

22 

65 

11-o285o4 

3 9 

22 

970947 

22-38 

998092 

• 20 

972805 

22 

57 

027145 

38 

23 

972289 

22 -3l 

998080 

• 20 

974209 

22 

5i 

025791 

3 7 

24 

973628 

22-24 

998068 

• 20 

975560 

22 

44 

024440 

36 1 

25 

974962 

22-17 

998056 

• 20 

976906 

22 

3 7 

023094 

35 

26 

976293 

22-10 

998044 

-20 

978248 

22 

3o 

021762 

^4 ; 

2*7 

977619 

22 • o3 

998032 

•20 

979586 

22 

23 

020414 

33 

28 

978941 

21.97 

998020 

•20 

980921 

22 

17 

019079 

32 

2 9 

980259 

21-90 

998008 

-20 

982261 

22 

10 

01 7749 

3i 

3o 

981570 

21-83 

997996 

•20 

983577 

22 

04 

016423 

3o 

3i 

8-982883 

21-77 

9.997985 

•20 

8•984899 

21 

97 

11-oi5ioi 

29 i 

32 

984189 

21-70 

997972 

•20 

986217 

21 

91 

013783 

28 

33 

985491 

21-63 

997959 

•20 

987532 

21 

84 

012468 

27 

34 

986789 

21-57 

997947 

•20 

988842 

21 

78 

011158 

26 

35 

988083 

21 -5o 

9979 33 

•21 

990149 

21 

7i 

ooo85i 

25 > 

36 

989374 

21-44 

997922 

-21 

991451 

21 

65 

008549 

24 1 

3 7 

990660 

21-38 

997910 

•21 

992750 

2! 

58 

007250 

23 

38 

991943 

21 - 31 

997807 

•21 

994045 

21 

52 

006955 

22 

3 9 

993222 

21-25 

997880 

•21 

995337 

21 

46 

004663 

21 

4o 

994497 

21-19 

997872 

•21 

996624 

21 

40 

003376 

20 

4i 

8-995768 

21 -1 2 

9-097860 

•21 

8-997908 

21 

34 

11-002092 

IQ 

42 

997036 

21 -06 

997847 

•21 

999188 

21 

27 

000812 

l8 

43 

998299 

21-00 

997835 

•21 

9-ooo465 

21 

21 

10-999535 

17 

44 

999560 

20 -o 4 

997822 

•21 

001738 

21 

i5 

998262 

l6 

45 

9-000816 

20-87 

997809 

•21 

003007 

21 

°2 

996993 

i5 

46 

002069 

20-82 

997797 

•21 

004272 

21 

o3 

995728 

14 

47 

oo33i8 

20-76 

997784 

•21 

oo5534 

20 

97 

994466 

i3 

48 

004563 

20-7© 

997771 

-21 

006792 

20 

91 

993208 

12 

4 9 

oo58o5 

20-64 

9977D8 

• 21 

008047 

20 

85 

991953 

11 

5 o 

007044 

20-58 

997745 

•21 

009298 

20 

80 

990702 

13 

5i 

9-008278 

20-52 

9-997732 

•21 

9-010546 

20 

74 

10-989454 


52 

009310 

20-46 

997719 

•21 

011790 

20 

68 

988210 

8 

53 

010737 

io-4o 

997706 

•21 

qi 3 oji 

20 

62 

986969 

7 

54 

011962 

20-34 

997693 

-22 

014268 

20 

56 

9 85 7 32 

6 

55 

oi 3 i 82 

20-20 

997600 

-22 

oi 55 o 2 

20 

5i 

984498 

5 

56 

014400 

20-25 

997667 

•22 

016732 

20 

45 

983268 

4 

s ~. 

oi 56 i 3 

20-17 

997654 

•22 

017959 

20 

40 

982041 

3 

5$ 

016824 

20-12 

997641 

-22 

019183 

20 

33 

980817 

2 

69 

qi 8 o 3 i 

20-06 

997628 

•22 

020403 

20 

28 

979597 

1 

60 

019135 

20-00 

997614 

•22 

021620 

20 

23 

978380 

0 J 


Cot in e 

D. 1 

Sine i 


Cotang. 

r 

>. 

Tang. 



{84 DEGREES.) 










































£4 (6 DECREES.) A TABLE OF LOGARITHMIC 


; m 

Sine 

IX 

Cosine 

IX 

Tang'. 

IX 

Cotang. 

■ --- 

' 0 

9-019235 

20-00 

9-997614 

.22 

9.021620 

20-23 

10-978380 

6a f 

I 

020435 

19-95 

997601 

•22 

022834 

20-17 

977166 

69 

2 

021632 

19-89 

19-84 

997688 

•22 

024044 

20-11 

976956 

5» 

3 

022825 

997574 

•22 

025251 

>0-06 

974749 

57 

1 4 

024016 

19-78 

997561 

•22 

026455 

20-00 

97354D 

56 

, 5 

025203 

19-73 

997547 

•22 

027655 

I9-9 5 

972345 

55 ' 

6 

026386 

19-67 

997534 

•23 

028852 

19-90 

971148 

54 

7 

027067 

19-62 

997620 

•23 

o3oo46 

19-85 

960954 

968763 

967675 

53 

8 

028744 

19-57 

997607 

•23 

o31237 

>9-79 

52 

0 

029918 

19-5i 

997493 

•23 

o32425 

19-74 

5i 

i ic 

o31089 

j 9*47 

99748o 

•23 

033609 

19-69 

966391 

Do 

ii 

9 -o 32257 

I9-4 i 

9-997466 

-23 

9-034791 

19-64 

10-965209 

49 - 

' 12 

o3342i 

19-36 

997462 

•23 

086969 

19-58 

964031 

48' 

! i3 

o34582 

i9-3o 

997439 

•23 

037144 

i 9 -D3 

962856 

47 

>4 

o3d74i 

19-25 

997426 

-23 

o383i6 

19-48 

961684 

46 

1 ID 

036896 

19-20 

997411 

•23 

039485 

I9-43 

960D1D 

45 

16 

o38o48 

19 • 15 

997397 

997383 

• 23 

040651 

19-38 

9Dq349 

44 

1 17 

039197 

19-10 

• 23 

041813 

I9-33 

908187 

43 

i 18 

040342 

19-05 

997369 

•23 

042973 

19-28 

967027 

42 

19 

o4i485 

18.99 

997355 

•23 

04413o 

19-23 

966870 

41 

20 

042625 

18-94 

997341 

•23 

045284 

19-18 

964716 

4a 

21 

9-043762 

18-89 

9-997327 

•24 

9-046434 

19-13 

10-953566 

39 

22 

1 23 

04489D 

046026 

18-84 

18-79 

997313 
697299 

•24 

•24 

047582 

048727 

049860 

19-08 

19-03 

952418 
951273 

38 

3? 

1 24 

o47i54 

18-75 

99728D 

• 24 

18-98 

95oi 31 

36 

2D 

048279 

18-70 

997271 

•24 

o5ioo8 

13-93 

948992 

35 

; 06 

049400 

i8-65 

997257 

•24 

052144 

18-89 

947866 

34 

; 27 

o5o5io 

18-60 

997242 

•24 

053277 

18-84 

946723 
9455 q 3 

33 

! 28 

o5i635 

i8-55 

997228 

•24 

054407 

18-79 

32 

i 29 

052749 

i8-5o 

997214 

• 24 

o55535 

18-74 

944465 

3i 

j 3o 

o538D9 

i8-45 

997199 

• 24 

o56659 

18-70 

943341 

3o 

I 3i 

9-054966 

1S - 41 

9.997185 

•24 

9-057781 

18-65 

10-942219 

20; 

1 32 

056071 

18-36 

997170 

•24 

058900 

18-69 

941100 

28 

! 33 

057172 

i8-3i 

997156 

•24 

060016 

i8-5D 

939984 

938870 

27 

1 3 4 

058271 

18-27 

997141 

•24 

061i3o 

i8-5i 

26 

! 35 

059367 

18-22 

997127 

•24 

062240 

18-46 

937760 

25 

36 

060460 

18-17 

997 112 

•24 

o63348 

18-42 

936652 

24 

37 

o6i55i 

18 • 13 

997008 

•24 

064453 

18-37 

935547 

23 

! 38 

062639 

18-08 

997083 

•25 

065556 

i8-33 

934444 

22 

! 39 

063724 

18-04 

997068 

•25 

o66655 

18-28 

933345 

21 

; 40 

064806 

17-99 

997063 

•25 

067752 

18-24 

932248 

20 

! 41 

9-o65885 

17-94 

9-997° 3 9 

•25 

9-068846 

18-19 

io-93ii54 

19 

42 

066962 

17-90 

997024 

•25 

069938 

18 -15 

930062 

18 

43 

o68o36 

17-86 

997009 

•25 

071027 

18-10 

928973 

*7 

44 

069107 

17-81 

996994 

•25 

0721i3 

18-06 

927887 

16 

43 

070176 

*7 "77 

996979 

•25 

078197 

18-02 

926808 

i5 

46 

071242 

17-72 

996964 

•25 

074278 

17-97 

925722 

U 

1 47 

072306 

17-68 

996949 

•25 

D75356 

17-93 

924644 

i3 

48 

073366 

17-63 

996934 

•25 

076432 

17-89 

923568 

12 

49 

074424 

17-59 

996919 

•25 

077606 

17-84 

922495 

11 

5o 

075480 

!7-5 d 

996904 

•25 

078576 

17-80 

921424 

ID 

5i 

c-076533 

17-5o 

9.996889 

•25 

9•079644 

17-76 

10-920356 

2 

52 

077583 

17-46 

996874 

•25 

080710 

17.72 

919290 

8 

! 53 

078631 

17-42 

996868 

•25 

081773 

17-67 

918227 

7 

i 34 

079676 

17-38 

996843 

•25 

082883 

17-63 

917167 

0 

55 

080719 

17-33 

996828 

•2D 

083891 

17-59 

916109 

9i5o53 

5 

56 

081759 

17-29 

996812 

• 26 

084947 

17-5 d 

4 

1 57 

082797 

17 • 2D 

996797 

• 26 

086000- 

17 • 51 

914000 

3 

1 58 

083832 

17*21 

996782 

•26 

087050- 

17-47 

912960 

a 

59 

084864 

17-17 

996766 

• 26 

088098 

I7-43 

911902 

1 

60 

086894 

17 • 13 

996761 

• 26 

089144 

17-38 

910806 

0 


Cosine 

D, 

Sine 


Cotang. 

D, 

Tang. 

M. 


(83 Q-EGRKES.) 


























































SINES AND TANGENTS. (7 DEGREES.) 21 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-085894 

17-13 

9-996751 

• 26 

9*089:44 

17-38 

10-910866 

60 

i 

086922 

17-09 

996735 

• 26 

09018; 

17.34 

900813 

5o 

2 

087947 

17-04 

996720 

.26 

09122S 

I7-3 o 

908772 

58 

3 

088970 

17-00 

996704 

• 26 

092266 

17-27 

907734 

57 

4 

089990 

16-96 

996688 

• 26 

093302 

17*22 

906698 

56 

5 

091008 

16-92 

996673 

• 26 

094336 

17-19 

906664 

55 

6 

092024 

16.88 

996657 

• 26 

095367 

17 • i5 

904633 

54 

7 

093037 

16-84 

996641 

• 26 

096395 

17*11 

9 o 36 o 5 

53 

8 

094047 

16-80 

996625 

• 26 

097422 

17*07 

902678 

62 

9 

095o56 

16-76 

996610 

• 26 

098446 

17-03 

901554 

5i 

to 

096062 

16-73 

996594 

• 26 

099468 

16-99 

900532 

5o 

11 

9-097065 

16-68 

9-996578 

•27 

9-100487 

16-96 

10-899513 

49 

12 

098066 

i6-65 

996562 

•27 

ioi 5 o 4 

16-91 

898496 

48 

i3 

099065 

16-61 

996546 

•27 

io25i9 

16-87 

897481 

47 

14 

100062 

16 -57 

996530 

•27 

io 3532 

16-84 

896468 

46 

i5 

ioio56 

16-53 

996514 

.27 

104542 

16-80 

895458 

45 

16 

102048 

16-49 

996498 

•27 

io555o 

16-76 

894460 

44 

*7 

io 3 o 37 

i 6-45 

996482 

•27 

io6556 

16-72 

893444 

43 

18 

104025 

16 • 4 f 

996465 

•27 

107559 

16-69 

892441 

42 

*9 

ioSoio 

i6-38 

996449 

•27 

io856o 

16.65 

891440 

4i 

20 

105992 

i 6-34 

996433 

•27 

109559 

16-61 

890441 

4o 

21 

9-106973 

i 6-3 o 

9.996417 

•27 

9-1io556 

16 • 58 

10-889444 

39 

22 

107951 

16-27 

996400 

.27 

11155 

i6-54 

888449 

38 

23 

108927 

i 6-23 

996384 

•27 

112643 

i6-5o 

887457 

37 

24 

109901 

i6- 19 

996368 

•27 

t13533 

16-46 

886467 

36 

25 

110873 

16-16 

996351 

•27 

114521 

i 6-43 

886479 

35 

26 

111842 

16-12 

996335 

•27 

115507 

16-39 

8844 q 3 

34 

27 

112809 

16-08 

996318 

•27 

116491 

i 6-36 

883509 

33 

28 

113774 

16-o5 

996302 

.28 

117472 

i 6-32 

882528 

32 

2 9 

114737 

16-01 

996285 

• 28 

118462 

16 • 29 

881548 

3i 

3o 

1156g8 

i 5-97 

996269 

-28 

119429 

i 6-25 

880671 

3o 

3i 

9-1i6656 

15-94 

9-996252 

.28 

9-120404 

i6- 22 

10-879696 

20 

32 

117613 

i 5-90 

996235 

.28 

121377 

16-18 

878623 

28 

33 

118567 

*5-87 

996219 

.28 

122348 

16 • 15 

877652 

27 

34 

119519 

15-83 

996202 

.28 

123317 

16-11 

876683 

26 

35 

120469 

i5-8o 

996185 

.28 

124284 

16-07 

875716 

25 

36 

121417 

15-76 

996168 

.28 

125249 

16-04 

874751 

24 

37 

122362 

s 5 - 73 

996151 

.28 

126211 

16-01 

878789 

23 ; 

38 

1233 o 6 

15-69 

996134 

.28 

127172 

i5*97 

872828 

22 ] 

39 

124248 

i 5-66 

996117 

.28 

i28i3o 

15-94 

871870 

21 

40 

125187 

i 5-62 

996100 

.28 

129087 

15-91 

870913 

20 

4i 

9-126125 

i 5-59 

9*996083 

• 29 

9-i 3 oo 4 i 

£ 5 • 87 

10-869959 

f 9 

42 

127060 

i 5-56 

996066 

• 29 

130994 

15-84 

869006 

18 

43 

127993 

i5-5a 

996049 

.29 

131944 

15 • 81 

868o56 

17 

44 

128925 

i 5»49 

996032 

• 29 

132893 

*5*77 

867107 

16 

45 

129854 

15 * 45 

996015 

•29 

13383 9 

15 • 74 

866161 

i5 

46 

130781 

15 - 42 

995998 

•29 

134784 

16-71 

865216 

14 

47 

181706 

t5-3o 

995980 

.29 

135726 

15-67 

864274 

i3 

48 

i 3263 o 

i5.35 

993963 

-29 

136667 

16-64 

863333 

12 

49 

i 3355 i 

i 5-32 

993946 

• 29 

137605 

i5-6i 

862396 

11 

5o 

134470 

i 5*29 

995928 

.29 

138542 

15 - 5S 

86 i 458 

10 

5i 

9-i 35387 

i 5-25 

9*99 5on 

.29 

9•139476 

15 - 55 

io- 86 o 524 

3 

52 

i363o3 

15 • 22 

995894 

•29 

140409 

15 • 51 

869691 

8 

53 

137216 

i5-19 

995876 

.29 

i 4 i 34 o 

15-48 

85866o 

7 

54 

138128 

i5-16 

995869 

.29 

142269 

i 5-45 

85773i 

6 

55 

139037 

15 • 12 

996841 

-29 

143196 

i 5-42 

8568o4 

5 

56 

189944 

15-09 

996823 

.29 

144121 

15-3o 

855879 

4 


140860 

i5-o6 

996806 

.29 

i 45 o 44 

15 • 35 

864956 

3 


141734 

i5-o3 

996788 

-29 

146966 

15 - 32 

854 o 34 

2 

59 

142655 

i5-oo 

995771 

.29 

146885 

15-29 

853 i i5 

1 

60 

143555 

14*96 

995753 

• 29 

147803 

i5-26 

852197 

0 ! 


Cosine 

D. 1 

Sine 


Cotang. 

D. 

lang. 

MJ 


(82 DEGREE8.) 













































































(8 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9*143555 

14 

96 

0*995753 

•3o 

9*147803 

i5 

26 

io»852i97 

60 

i 

144453 

14 

93 

995735 

• 3o 

148718 

i5 

23 

851282 

59 

2 

145349 

14 

90 

995717 

• 3o 

149632 

i5 

20 

85o368 

58 

3 

146243 

14 

87 

995699 

•3o 

15o544 

i5 

«7 

849466 

57 

4 

147136 

14 

84 

995681 

•3o 

151454. 

i5 

U 

848546 

56 

5 

148026 

14 

81 

995664 

•3o 

152363 

i5 

11 

847637 

55 

6 

i 48 qi 5 

14 

78 

996646 

*3o 

163269 

i5 

08 

846731 

54 

7 

149802 

14 

7 5 

995628 

•3o 

154174 

i5 

o5 

845826 

53 

8 

i5o686 

14 

72 

995610 

*3o 

155077 

i5 

02 

844928 

52 

9 

151069 

14 

69 

995591 

•3o 

155978 

14 

99 

844022 

5i 

lo 

iD 245 i 

14 

66 

995573 

•3o 

156877 

14 

96 

843123 

5o 

n 

9 • i* J33o 

14 

63 

9*995555 

•3o 

9* 167775 

14 

93 

10*842225 

49 

12 

i54208 

14 

60 

995537 

• 3o 

168671 

14 

oo 

841329 

48 

i3 

i55o83 

14 

57 

995519 

• 3o 

169665 

14 

87 

84043^ 

47 

U 

i 55 o 57 

14 

54 

9955 oi 

•3i 

160457 

U 

84 

839543 

46 

i5 

i 5683 o 

14 

5i 

996482 

• 3i 

161847 

14 

81 

838653 

45 

16 

157700 

14 

48 

995464 

•3i 

162236 

14 

79 

837764 

44 

»7 

15856o 

14 

45 

995446 

•3i 

i63i23 

14 

76 

S36877 

43 

18 

159435 

14 

42 

996427 

•3i 

164008 

14 

73 

835992 

42 

19 

i6o3oi 

14 

39 

995409 

•3i 

164892 

14 

70 

835108 

4i 

20 

161164 

14 

36 

996390 

•3i 

166774 

14 

67 

834226 

40 

21 

9*162025 

14 

33 

9*995372 

• 3x 

9*166604 

14 

64 

10*833346 

39 

22 

162885 

14 

3o 

995353 

• 3i 

167532 

14 

61 

832468 

38 

23 

163743 

14 

27 

995334 

• 3i 

168409 

14 

68 

831691 

37 

24 

164600 

14 

24 

995316 

*3i 

169284 

14 

55 

880716 

36 

25 

165454 

14 

22 

996297 

• 3i 

170157 

14 

53 

829843 

35 

26 

166307 

14 

19 

996278 

• 3i 

171029 

14 

5o 

828971 

34 

27 

167159 

14 

16 

995260 

• 3i 

171899 

14 

47 

828101 

33 

28 

168008 

14 

i3 

995241 

•32 

172767 

14 

44 

827233 

32 

29 

168856 

14 

10 

995222 

*32 

173634 

14 

42 

826866 

3i 

3o 

169702 

14 

°7 

9952o3 

*32 

174499 

14 

3 9 

8255 oi 

3o 

3i 

9*170547 

14 

o5 

9*995184 

•32 

9*175362 

14 

36 

10*824638 


32 

171389 

14 

02 

995165 

*32 

176224 

14 

33 

823776 

28 

33 

172230 

i3 

99 

996146 

•32 

177084 

14 

3i 

822916 

27 

34 

173070 

i3 

96 

995127 

•32 

177942 

14 

28 

822068 

26 

35 

173908 

i3 

94 

995108 

•32 

178799 

14 

25 

821201 

25 

36 

174744 

i3 

91 

995089 

•32 

179605 

14 

23 

820345 

24 

37 

175578 

i3 

88 

995070 

•32 

18 o 5 o 8 

14 

20 

819492 

23 

38 

176411 

i3 

86 

995o5i 

•32 

18136o 

14 

17 

818640 

22 

3 9 

177242 

1? 

83 

996032 

•32 

182211 

14 

i5 

817789 

21 

4o 

178072 

i3 

80 

995013 

•32 

i83o59 

14 

12 

816941 

20 

41 

9*178900 

i3 

77 

9*994993 

•32 

9 * 183907 

14 

09 

10*816093 

10 

42 

179726 

i3 

74 

994974 

•32 

184752 

14 

07 

815248 

l8 

43 

i8o55i 

i3 

72 

994955 

•32 

186697 

14 

04 

8 i 44 o 3 

11 

44 

181374 

i3 

69 

994935 

•32 

1 86489 

14 

02 

81356i 

l6 

45 

182196 

i3 

66 

994916 

.33 

187280 

i3 

99 

812720 

i5 

46 

i83oi6 

i3 

64 

994896 

.33 

188120 

i3 

96 

811880 

14 

47 

183834 

i3 

61 

994877 

.33 

188968 

i3 

93 

811042 

i 3 

48 

1 8465 1 

i3 

5> 

994807 

.33 

189794 

i3 

91 

810206 

13 

49 

1 85466 

i3 

5b 

994838 

.33 

1 90629 

i3 

89 

809371 

11 

5o 

186280 

i3 

53 

994818 

.33 

191462 

i3 

86 

8o8538 

10 

5i 

9*187092 

i3 

5i 

9*994798 

•33 

9*192294 

i3 

84 

10*807706 

9 

52 

187903 

i3 

48 

994779 

.33 

193124 

i3 

81 

806876 

8 

53 

188712 

i3 

46 

994709 

.33 

1 93953 

i3 

79 

806047 

7 

54 

189510 

i3 

43 

994739 

•33 

194780 

i3 

76 

8 o 5220 

6 

55 

190326 

i3 

41 

994719 

• 33 

196606 

i3 

74 

804394 

5 

56 

191i3o 

i3 

38 

994700 

• 33 

196430 

i3 

7 1 

803570 

4 

57 

191933 

i3 

36 

994680 

• 33 

107253 

i3 

69 

802747 

3 

58 

192734 

i3 

33 

994660 

• 33 

198074 

i3 

66 

801926 

ft 

59 

193634 

i3 

3o 

994640 

*33 

198894 

i3 

64 

801106 

1 

60 

194332 

i3* 

28 

994620 

• 33 

199713 

1 3 

61 

800287 

0 

j 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. ] 


(81 DEGREES.) 











































SINES AND TANGENTS. (9 DEGREE.) 


27 


M. 

Sine 

D. 

Cosine 

D. 

Tang., 

D. 

Cotang. 


o 

9*194332 

i 3*28 

9*994620 

• 33 

9*199713 

i 3 * 6 i 

10*800287 

60 

i 

195129 

i 3*26 

1 994600 

*33 

200629 

1 3 • 5 g 

799471 

59 

2 

195923 

1 3 • 23 

99458 o 

• 33 

201347 

i 3*56 

798655 

58 

3 

196719 

1 3 • 21 

99456 o 

• 34 

202169 

i3*54 

797841 

5 ? 

4 

197511 

1 3 • 1 8 

994540 

•34 

202971 

1 3 - 52 

797029 

56 

5 

198302 

1 3 • 16 

994519 

• 34 

203782 

1 3 • 49 

796218 

55 

6 

199091 

1 3 • 1 3 

994499 

•34 

204692 

i 3 *47 

796408 

54 

7 

199879 

1 3 • 11 

994479 

• 34 

205400 

i 3*46 

794600 

53 

8 

200666 

i 3 *o 8 

994459 

• 34 

206207 

i 3*42 

793793 

52 

9 

201461 

i 3 *o 6 

994438 

• 34 

207018 

i 3 * 4 o 

792987 

5 i 

10 

202234 

i 3 *o 4 

994418 

• 34 

207817 

1 3 • 38 

792183 

5 o 

n 

( 9*203017 

i 3 *oi 

9*994397 

*34 

9*208619 

1 3 • 35 

io* 79 i 38 i 

49 

12 

203797 

12*99 

994377 

*34 

209420 

1 3 - 33 

700080 

48 

i 3 

204577 

12*96 

994357 

•34 

210220 

1 3 • 3 1 

789780 

788982 

47 

14 

205354 

12*94 

994336 

•34 

211018 

1 3 - 28 

46 

i 5 

2 o 6 i 3 i 

12*02 

9943 1 6 

•34 

21181 5 

i 3*26 

788185 

45 

16 

206906 

I2*»9 

994295 

•34 

212611 

1 3 • 24 

787389 

44 

*7 

18 

207679 

208452 

I2-87 

12*85 

994274 

994254 

•35 

•35 

2 i 34 o 5 

214108 

1 3 • 2 1 

1 3 • 1 9 

786696 

785802 

43 

42 

! 9 

209222 

12*82 

994233 

•35 

2:4989 

1 3 • 1 7 

785 oii 

4 i 

20 

209992 

12*80 

994212 

•35 

215780 

1 3 • 1 5 

784220 

40 

21 

9 *210760 

12*78 

9-994191 

*35 

9 * 2 i 6568 

1 3 • 12 

io *783432 

3 9 

22 

211 526 

12*75 

994171 

• 35 

217356 

i 3 * 10 

^82644 

38 

23 

212291 

12*73 

994i 5 o 

• 35 

218142 

i 3 *o 8 

781858 

37 

24 

2i3o55 

12*71 

994129 

994108 

*35 

218926 

i 3 *o 5 

781074 

36 

25 

21 38 18 

12*68 

• 35 

219710 

i 3 *o 3 

780290 

35 

26 

214579 

12*66 

994087 

• 35 

220492 

i 3 *oi 

779508 

778728 

34 

2-7 

215338 

12*64 

994066 

• 35 

221272 

12 -99 

33 

28 

216097 

216854 

12 • 61 

994045 

•35 

222062 

12*97 

777948 

32 

29 

12*59 

994024 

• 35 

222830 

12*94 

777170 

3 i 

3 o 

217609 

12*57 

994oo3 

•35 

223606 

12*92 

77 63 94 

3 o 

3 i 

9* 2 i 8363 

12*55 

9*993981 

*35 

9*224382 

12*90 

10*775618 

29 

32 

219116 

12*53 

993960 

*35 

2 25 1 56 

12 • 88 

774844 

28 

33 

219868 

I 2 * 5 o 

998989 

993918 

993896 

*35 

225929 

12*86 

774071 

27 

34 

220618 

12*48 

*35 

226700 

12*84 

7733oo 

26 

35 

221367 

12*46 

*36 

227471 

12 • 81 

772629 

25 

36 

22211 5 

12*44 

993875 

*36 

228289 

12*79 

771761 

24 

37 

222861 

12*42 

993864 

*36 

229007 

12*77 

770993 

23 

38 

223606 

12*39 

993832 

*36 

229778 

12*75 

770227 

22 

3 9 

224349 

12*37 

993811 

*36 

230589 

12*73 

769461 

21 

4 o 

225092 

12*36 

998789 

*36 

23 i 3 o 2 

12*71 

768698 

20 

4 i 

9*225833 

12*33 

9*993768 

*36 

9* 232 o 65 

12*69 

10*767935 

IQ 

42 

226573 

12 • 3 1 

998746 

•36 

232826 

12*67 

767174 

10 

43 

227311 

228048 

12*28 

993725 

•36 

233586 

12*66 

766414 

17 

44 

12*26 

993703 

*36 

234345 

12*62 

765656 

l6 

45 

228784 

12*24 

998681 

*36 

235 io 3 

12*60 

764897 

i 5 

46 

229618 

12*22 

9 g 366 o 

*36 

235 Sj 9 

12*58 

764141 

14 

47 

230252 

12*20 

993638 

*36 

2366 1 4 

12*56 

763386 

i 3 

48 

230984 

12* l8 

993616 

*36 

23 7 368 

12*54 

762632 

12 

49 

231714 

12 • l6 

993594 

•87 

238120 

12*52 

761880 

11 

5 o 

232444 

12*14 

993572 

•37 

238872 

I 2 * 5 o 

761128 

10 

5 : 

9*233172 

12*12 

9*99355o 

* 3 7 

9*239622 

12*48 

10*760378 

9 

52 

53 

233899 

234626 

12*09 

12*07 

993528 

9935 o 6 

•87 

.37 

240371 

241118 

12*46 

12*44 

759629 

758882 

8 

7 

54 

235349 

I 2 • 06 

993484 

•87 

24(865 

12*42 

758 i 35 

6 

55 

236073 

I 2 *o 3 

993462 

.37 

242610 

12*40 

757390 

5 1 

56 

236795 

12*01 

993440 

• 37 

243354 

12*33 

756646 

4 

5 ? 

237615 

ii *99 

993418 

.37 

244097 

12*36 

755903 

3 

58 

238235 

ii *97 

993396 

*87 

244889 

12*34 

755 i 6 i 

2 

59 

238953 

ii *95 

993374 

.37 

245579 

12*32 

754421 

1 

60 

239670 

11 *93 

993361 

* 3 7 

246319 

I 2 * 3 o 

75368 i 

0 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M.J 


(80 DEGREES,) 




























































28 (10 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

I). 

Cosine 

D. 

Tang. 

D. 

Cotang. 

1 

o 

9-239670 

11 -98 

9 - 99335 i 

* 3 7 

9*246319 

I2-3o 

io* 75368 i 

60 

i I 

24o386 

11*91 

993329 

.37 

247057 

12*28 

762943 

5 o 

2 ! 

241ioi 

11-89 

993307 

.37 

247794 

12*26 

752206 

58 

3 

241814 

11-87 

998285 

• 37 

24853o 

12*24 

751470 

57 

4 

242526 

n -85 

993262 

.37 

249264 

12-22 

750736 

56 

5 

243237 

n -83 

993240 

•37 

249998 

12-20 

750002 

55 

6 i 

243947 

11 • 81 

993217 

*38 

250760 

12- l8 

749270 

54 

1 

244656 

ii *79 

993196 

*38 

261461 

12*17 

748539 

53 

8 i 

245363 

ii *77 

993172 

• 38 

252191 

I 2 - 15 

747809 

52 

9 

246069 

ii *75 

993149 

*38 

252920 

1 2 - 13 

747080 

5 i 

IC 

246776 

ii *73 

993127 

*38 

253648 

12*11 

746352 

5 o 

11 

9-247478 

11*71 

9-993104 

*38 

9-254374 

12-09 

10*746626 

49 

12 

248161 

11-69 

993081 

*38 

255 ioo 

12-07 

744900 

48 

i 3 

248883 

11 *67 

993059 

*38 

255824 

12 -o 5 

744176 

47 

U 

249583 

ii *65 

993o36 

*38 

256547 

I 2 -o 3 

743453 

46 

i 5 

260282 

11 *63 

99301 3 

*38 

257269 

12-01 

742731 

45 

16 

250980 

11 • 61 

992990 

*38 

267990 

12-00 

742010 

44 

17 

251677 

11*59 

992967 

• 38 

258710 

11*98 

741290 

43 

18 

252376 

n -58 

992944 

*38 

259429 

11-96 

740571 

42 

' x 9 

253067 

ii *56 

992921 

*38 

260146 

11 *94 

739864 

4 i 

20 

253761 

ii *54 

992898 

*38 

260863 

11 *92 

739137 

40 

21 

9-264453 

11-52 

9-992875 

*38 

9-261578 

I I -GO 

10-738422 

3 9 

22 

255 144 

11 - 5 o 

992862 

*38 

262292 

11-89 

737708 

38 

23 

255834 

11*48 

992829 

* 3 9 

263 oo 5 

11-87 

736995 

37 

24 

256523 

11-46 

992806 

.39 

263717 

n -85 

7 36283 

36 

25 

257211 

11 -44 

992783 

• 3 g 

264428 

ii -83 

735572 

35 

26 

257898 

11*42 

992759 

• 3 9 

2661 38 

11 • 81 

734862 

34 

27 

258583 

11 *41 

992736 

* 3 9 

265847 

ii *79 

734 i 53 

33 

28 

269268 

11-39 

992713 

* 3 9 

266555 

11-78 

733445 

32 

29 

259951 

11 *37 

992690 

* 3 9 

267261 

11*76 

732739 

3 i 

3 o 

26 c 633 

n -35 

992666 

• 3 g 

267967 

ii *74 

732033 

3 o 

3 i 

9- 26 i 3 14 

n -33 

9-992643 

* 3 9 

9*268671 

11*72 

10*731329 

29 

32 

261994 

11 • 3 1 

992619 

* 3 9 

269376 

11*70 

730620 

28 

33 

262673 

11 - 3 o 

992696 

• 3 9 

270077 

11*69 

729923 

27 

34 

263351 

11-28 

992572 

• 3 9 

270779 

11 *67 

729221 

26 

35 

264027 

11-26 

992649 

* 3 9 

27 U 79 

11 *65 

728621 

25 

36 

264708 

II -24 

992620 

*3 9 

272178 

11*64 

727822 

24 

37 

265377 

11-22 

992601 

• 3 9 

272876 

11-62 

727124 

23 

38 

266061 

I I • 20 

992478 

• 40 

273573 

11 - 6o 

726427 

2 2 

3 g 

266723 

11-19 

992454 

• 4 o 

274269 

ii -58 

726731 

21 

4 o 

267895 

ii -,7 

992430 

•40 

274964 

11*67 

725o36 

20 

41 

9-268o65 

11 • 1 5 

9-992406 

•40 

9-275658 

11 *55 

10*724342 

IQ 

42 

268734 

11 - 1 3 

992382 

•40 

276351 

ii *53 

723649 

l8 

43 

269402 

ii*ii 

992359 

•40 

277043 

11 - 51 

722957 

17 

44 

270069 

11 • 10 

992330 

•40 

277734 

11 * 5 o 

722266 

10 

45 

270735 

11 - 08 

992311 

•40 

273424 

11 *48 

721676 

i 5 

46 

271400 

11 - 06 

992287 

•40 

2791i 3 

11*47 

*720887 

i 4 

47 

272064 

11 - o 5 

992263 

•40 

279801 

11 *45 

720199 

i 3 

48 

272726 

11 *o 3 

992239 

•40 

280488 

11 *43 

719612 

12 

49 

273388 

1 I -01 

992214 

•40 

281174 

11 *4i 

718826 

11 

5 o 

274049 

10-99 

992190 

•40 

28 i 858 

11 * 4 o 

718142 

10 

5 i 

9-274708 

10-98 

9-992166 

• 4 o 

9-282542 

n -38 

10-717458 

9 

52 

275867 

10-96 

992142 

• 40 

283225 

11 *36 

716775 

8 

53 

276024 

10-94 

992117 

• 4 i 

283907 

11 *35 

716093 

7 

54 

276681 

10-92 

992093 

• 4 i 

284088 

u -33 

715412 

1 6 

55 

277337 

10*91 

992069 

• 4 i 

286268 

11 - 3 1 

714732 

5 

56 

277991 

10-89 

992044 

• 4 i 

285947 

11 * 3 o 

714053 

4 

57 

278644 

10*8*7 

992020 

• 4 i 

286624 

11-28 

713376 

3 

58 

279297 

io-86 

991996 

•41 

287301 

11-26 

712699 

2 

59 

279948 

10*84 

99197 1 

• 4 i 

287977 

II -20 

71202S 

1 

| 60 

280099 

10-82 

991947 

• 4 i 

288662 

11*23 

711 348 

0 

1 

Cosine 

D. 

Sine 

I 

Co tang. 

D. 

Tang. 

M. 


(79 DEGREES.) 
































































SINES AND TANGENTS. (11 DEGREES.) 29 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-280599 

10-82 

9*991947 

.41 

9-288652 

11*23 

10*711348 

60 

i 

281248 

io-8i 

991922 

.41 

289326 

11*22 

710674 

5o 

1 

281897 

10.79 

991897 

• 41 

289999 

11*20 

710001 

58 

3 

282544 

io-77 

991873 

•41 

290671 

11 • l8 

709329 

57 

4 

283190 

10-76 

991848 

•41 

291342 

11*17 

708668 

56 

5 

283836 

10-74 

991823 

• 41 

292013 

11*10 

707987 

55 

6 

284480 

10-72 

991799 

• 41 

292682 

11 • 14 

707318 

54 

7 

285124 

10-71 

991774 

• 42 

293350 

11*12 

7o665o 

53 

8 

285766 

10-69 

991749 

.42 

294017 

I I • I I 

705983 

5a 

9 

286408 

10*67 

991724 

.42 

294684 

11*09 

7o5316 

5i 

10 

287048 

io-66 

991699 

.42 

295349 

11-07 

704651 

5o 

11 

9-287687 

10*64 

9-99i674 

•42 

9-296013 

11 - 06 

10*703987 

49 

la 

288326 

io-63 

991649 

• 42 

296677 

11 - 04 

703323 

48 

i3 

288964 

io*6i 

991624 

•42 

297339 

11 - o3 

702661 

47 

14 

289600 

10-5o 

991599 

•42 

298001 

1 I -01 

701999 

46 

i5 

290236 

10*58 

99i574 

•42 

298662 

11*00 

7oi338 

45 

16 

290870 

io*56 

991549 

•42 

299322 

10-98 

700678 

44 

17 

291504 

io-54 

991524 

•42 

299980 

10-96 

700020 

43 

18 

292137 

io*53 

991498 

•42 

3oo638 

10-95 

699362 

42 

19 

292768 

io*5i 

991473 

•42 

301296 

10-93 

698705 

4i 

20 

293399 

io*5o 

991448 

•42 

301901 

10-92 

698049 

4o 

21 

9-294029 

10*48 

9*991422 

•42 

9-302607 

10-90 

10*697393 

3 9 

22 

294650 

10-46 

991397 

.42 

3o326i 

10-89 

696739 

38 

23 

295286 

io*45 

991372 

•43 

303914 

10-87 

696086 

37 

24 

295918 

io*43 

991346 

•43 

804067 

io*86 

695433 

36 

25 

296739 

10*42 

991321 

•43 

3o52i8 

10-84 

694782 

35 

26 

297164 

io*4o 

991295 

•43 

805869 

io-83 

694131 

34 

27 

297788 

10*39 

991270 

•43 

3o65i9 

io-8i 

693481 

33 

28 

298412 

10*37 

99*244 

•43 

307168 

io-8o 

692832 

32 

29 

299034 

io*36 

991218 

• 43 

307815 

10-78 

692185 

3i 

3o 

299655 

10*34 

991193 

•43 

3o8463 

io*77 

691537 

3o 

3i 

9-300276 

10*32 

9.991167 

•43 

9-309109 

10*75 

10*690891 

29 

32 

300896 

io*3i 

99**41 

•43 

309764 

10*74 

690246 

28 

33 

3oi5i4 

10-20 

991115 

•43 

310398 

10*73 

689602 

27 

34 

3o2i32 

10-28 

991090 

•43 

311042 

10*71 

688968 

26 

35 

302748 

10-26 

991064 

•43 

311685 

10*70 

688315 

25 

36 

3o3364 

10-25 

99io38 

•43 

312327 

io*68 

687673 

24 

3? 

303979 

10-23 

991012 

•43 

312967 

10*67 

687033 

23 

38 

3o4793 

10-22 

990986 

•43 

3i36o8 

io-65 

686392 

22 

39 

306207 

10-20 

990960 

•43 

3i4247 

10-64 

686703 

21 

4o 

3o58i9 

io* 19 

990934 

•44 

314885 

10*62 

685i15 

20 

4i 

9-3o643o 

10*17 

9-99oqo8 

•44 

9•315523 

io*6i 

10*684477 

1 9 

42 

307041 

10* 16 

990882 

•44 

316159 

io-6o 

683841 

10 

43 

307650 

10* 14 

990855 

•44 

316790 

io*58 

683205 

*7 

44 

308259 

io* i3 

990829 

•44 

317430 

10*57 

682670 

l6 

45 

308867 

10* 1 I 

990803 

•44 

318064 

io*55 

681986 

i5 

46 

309474 

10*10 

990777 

•44 

318697 

io*54 

681Jo3 

14 

47 

310080 

10*08 

990750 

•44 

319329 

io*53 

680671 

i3 

48 

3io685 

10*07 

990724 

•44 

319961 

io*5i 

63oo3o 

12 

49 

311289 

io*o5 

990697 

•44 

320092 

io*5o 

6794OD 

11 

5o 

311897 

io*o4 

99067I 

•44 

321222 

10*48 

678778 

10 

5 i 

9-312495 

io*o3 

9-990644 

•44 

9*32185i 

io *47 

10*678149 

9 

52 

3 13097 

10*01 

9906i8 

•44 

322479 

io-45 

677521 

8 

53 

313698 

10-00 

990591 

•44 

323io6 

io-44 

676894 

7 

54 

314297 

9.98 

990565 

•44 

323733 

io-43 

676267 

6 

55 

314897 

9-97 

990538 

•44 

324358 

10-41 

676642 

5 

56 

3 15495 

9-96 

9905 11 

•45 

3249S3 

io-4o 

676017 

4 

^7 

316092 

9.94 

990435 

•45 

325607 

10*39 

674393 

3 

58 

3 1 6689 

9-93 

990468 

•45 

326231 

10*37 

673769 

2 

59 

317284 

9.91 

990431 

•45 

326853 

io*36 

673147 

1 

60 

317879 

9-90 

9904 >4 

•45 

327475 

io-35 

672625 

0 

LT. 

Cosine 

D. 

Sine 

L 

Cotang. 

D. 

Tan s- 

M. 


(78 DEGREES.) 


















































30 


(12 DEGREES., A TABLE OF LOGARITHMIC 


r M. 

Sice 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

i o 

u 

12 

13 

14 

15 

16 

»7 

18 

19 

20 

21 

22 

23 

24 

25 

26 
27 
20 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

3 9 

40 

4x 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

60 

9.317879 

3i84i3 

319066 
319658 
320249 

320840 

32i43o 

322019 

322607 

3 2 3194 
323780 

9.324366 
324 q 5 o 
325534 
326117 
326700 
327281 
327862 
328442 
329021 
329599 

9.330176 
330753 
331329 
331903 
332478 
333o5i 
333624 
334195 
334766 
335337 

9.335906 

336475 

337043 

337610 

338176 

338742 

339306 

339871 

340434 

340996 

9•34* 558 
342119 
342679 
343239 

343797 

3443 d 5 

344912 

345469 

346024 

346579 

9.347134 

347687 

348240 

348792 

349343 

349893 

350443 

350992 

35 i 04 o 

352 o 88 

- 

9.00 

9.08 
9.87 
9.86 

9.84 

9-83 

9.82 

9.80 
9-79 
9-77 
0*76 

9.75 

9-73 

9-72 

9.70 

9.69 

9.68 

9-66 

9-65 

9-64 

9-62 

9.61 
9-60 
9-58 

9.57 

9-56 

9-54 

9-53 

9-52 

9-5 o 

9.49 

9.48 

9.46 

9.45 

9-44 

9.43 

9.41 

9.40 

9.39 

9.37 

9*36 

9-35 

9.34 

9.32 

9 • 31 
9>3o 
9.29 
9.27 
9.26 

9*25 

9-24 

9.22 

9*21 

9*20 

9 #I 9 

9-17 

9.16 | 

9 • 15 

9-14 

9 * 13 
9.11 

9.990404 
990378 
990351 
990324 

990297 

990270 

990243 

990215 
990188 
990161 

990134 

9.990107 

990079 

990052 

990025 

989997 

989970 

989942 

989915 

989887 

989860 

9.989832 

989804 

9 8 9777 

989749 

989721 

989693 

989665 

989637 

989609 

989582 

9.989653 

989525 

989497 

989469 

989441 

989413 

989L84 

989356 

089328 

989300 

9-989271 

989243 

989214 
989186 
989157 
989128 
989100 
989071 
989042 
989014 

9-988986 
988956 
988927 
988898 
988869 
988840 
q888i1 
988782 

988753 

988724 

•45 
•45 
•45 
•45 
•45 
•45 
•45 
•45 
•45 
•45 
• 45 

•46 

.46 

.46 

.46 

•46 

.46 

•46 

.46 

.46 

•46 

•46 

.46 

.46 

•47 

•47 

*47 

•47 

•47 

•47 

•47 

•47 

•47 

•47 

•47 

•47 

•47 

•47 

•47 

•47 

•47 

*47 

•47 

*47 

'47 

•47 

•48 

•48 

•48 

•48 

•48 

•48 

•48 

•48 

•48 

•48 

•48 

•49 

•49 

.49 

•49 

9.327474 
328095 
328715 
329334 
329953 
33067c 
331187 
33i8o3 
3324 i 8 
333o33 
333646 

9.334259 

334871 

335482 

336093 

336702 

337611 

337919 

338527 

339133 

339739 

9■34o344 
340948 
341662 
342155 
342757 
343358 
343958 

344658 

346157 

345756 

9.346353 

346949 

347645 

348141 

348735 

349629 

349922 

360614 

351106 
351697 

9.352287 

352876 

353465 

354o53 

354640 

355227 

3558 i 6 

3563o8 

356982 

357666 

9.358149 

358731 

359613 

359893 

360474 

36io53 

36 i 632 

362210 

362787 

363364 

io-35 
10-33 
10-32 
10.3o 
10-29 
10-28 
10-26 
10-25 
10-24 
10-23 
10-21 

10-20 
10- 19 
10-17 
10- 16 
io-15 
io-13 
10-12 

IO- 11 

IO-10 

10-08 

10-07 

10-06 

10-04 

io-o3 

10-02 

10-00 

9.90 
9.98 

9'97 

9.96 

9.94 

9 - 9 3 

9-92 

9.9 1 

9-8j 

9*8o 

9-85 

9-83 

9-82 

9-81 

9.80 
9'79 

9*77 

9-76 

9-75 

9'74 

9-73 

9-7 1 

9-70 

9.60 

9-68 

9-67 

9-66 

9-65 

9-63 

9-62 

9-61 

9-60 

10-672526 

671905 

671285 

670666 

670047 

669430 

6688i3 

668197 

667682 

666967 

666354 

10-666741 

666129 

664518 

663907 

663298 

662609 

662081 

661473 

660867 

660261 

10-659656 

659062 

658448 

657845 

657243 

666642 

656o42 

655442 

654843 

654245 

10-653647 

653o5i 

652455 

65i85o 

65i265 

650671 

650078 

649486 

648894 

6483o3 

10-647713 

647124 

646535 

645947 

645460 

644773 

644187 

6436o2 

643 oi 8 

642484 

1 0 - 64185i 
641269 
640687 
640107 
639526 
638947 
638368 
687790 
637213 
636636 

60 

5p 

58 

57 

56 

55 

54 

53 

52 

5i 

5o 

49 

48 

2 

45 

44 

43 

42 

4i 

4o 

3 9 

38 

37 

36 

35 

34 

33 

32 

3i 

3o 

20 

28 

27 

26 

25 

24 

23 

22 

21 

20 

;g 

17 

16 

i5 

i4 

i3 

12 

11 

10 

? 

5 

4 

3 

2 

1 

0 


Cosine 

D. 

Sine 

Cotang. 

D. Tang. 

M. 


(77 DEGREES.) 



















































s. 




SINES AND TANGENTS. (13 DEGREES.) SI 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-352 o 88 

9*n 

q 988724 

.49 

9*363364 

9* 60 

10•636636 

60 

i 

352635 

9*10 

988696 

•49 

363940 
364516 

9*5 9 

636o6o 

5o 

2 

35318i 

9*oq 

988666 

•49 

9*58 

635485 

58 

3 

353726 

9* 08 

988636 

•49 

866090 

9.57 

634910 

57 

4 

354*71 

9*07 

988607 

.49 

365664 

9-55 

634336 

56 

5 

3548 i 5 

g*o5 

988578 

•49 

366237 

9*54 

633763 

55 

6 

355358 

9*04 

988648 

•49 

3668io 

9*53 

633190 

54 

7 

355901 

9 *o 3 

988519 

.49 

367382 

9*52 

632618 

53 

8 

356443 

9*02 

988489 

• 49 

367953 

9 • 51 

632047 

52 

9 

356q84 

0*01 

988460 

.49 

368524 

9*5 o 

631476 

5i 

10 

367624 

8*99 

988430 

•49 

369094 

9*49 

630906 

5o 

11 

9*358o64 

8*98 

9*988401 

.49 

9 *369663 

9.48 

io* 63 o 337 

49 

12 

3586o3 

8*97 

988371 

.49 

370232 

9*46 

629768 

48 

i3 

3 5g 14 x 

8*96 

988342 

.49 

370799 

9*45 

629201 

47 

14 

359678 

8* 9 5 

988312 

• 5o 

371367 

9.44 

628633 

46 

i5 

360215 

8* 9 3 

988282 

• 5o 

371933 

9*43 

628067 

45 

16 

360762 

8*92 

988252 

• 5o 

372499 

9-42 

627601 

44 

*7 

361287 

8*91 

988223 

• 5o 

373064 

9*41 

626936 

43 

18 

361822 

8*90 

988193 

• 5o 

373629 

9.40 

626371 

42 

*9 

362356 

8*89 

9 88i63 

• 5o 

374193 

9 * 3o 

626807 

41 

20 

362889 

8*88 

9 88 i 33 

• 5o 

374756 

9*38 

626244 

4o 

21 

9*363422 

8*87 

9*988103 

• 5o 

9*375319 

9*37 

10*624681 

3 9 

22 

363g54 

8*85 

988073 

•5o 

3 7 588i 

9*35 

624119 
623558 

38 

23 

364485 

8*84 

988048 

• 5o 

376442 

9*34 

37 

U 

365oi6 

8*83 

988013 

*5o 

377003 

9*33 

622997 

622407 

36 

25 

355546 

8*82 

987988 

• 5o 

377568 

9*32 

35 

26 

366075 

8 • 81 

987953 

*5o 

378122 

9 • 31 

621878 

34 

27 

3666o4 

8* 80 

987922 

987892 

• 5o 

3 7 868 i 

9*3 o 

621319 

33 

28 

367131 

8*79 

*5o 

379289 

9*29 

620761 

32 

3o 

367669 

368 i 8 d 

8*77 

8 • 76 

987862 

987832 

• 5o 

• 5i 

379797 

38o354 

9*28 

9*27 

620203 

619646 

3i 

3o 

3i 

9*368711 

8*75 

9*987801 

*5i 

9*380910 

9.26 

10*619090 

6 i 8534 

29 

32 

369236 

8*74 

987771 

• 5i 

381466 

9*25 

28 

33 

369761 

8 - 73 

987740 

• 5i 

382020 

9*24 

617980 

27 

34 

370285 

8*72 

987710 

• 5i 

382576 

9*23 

617426 

26 

35 

370808 

8*71 

987679 

• 5i 

383i29 

9-22 

616871 

25 

36 

37133o 

8*70 

987649 

*5i 

383682 

9*21 

616318 

24 

37 

371862 

8*69 

9S7618 

*5i 

384234 

9*20 

615766 

23 

38 

372373 

8*67 

987588 

*5i 

384786 

9*io 

615214 

22 

39 

372894 

8*66 

987557 

• 5i 

385337 

9 * 1 8 

614663 

21 

4o 

373414 

8*65 

987626 

• 5i 

385888 

9-n 

614112 

20 

4t 

9*373933 

8*64 

9*987496 

• 5i 

9*386438 

9 • 15 

io* 6 i 3562 

IO 

42 

374452 

8*63 

987465 

• 5i 

386987 

9 *i 4 

6 i 3 oi 3 

l8 

43 

37497° 

8*62 

987434 

• 5i 

387536 

9* i3 

612464 

17 

44 

375487 

8*6i 

987403 

•52 

388084 

9-12 

611916 

l6 

45 

376008 

8* 60 

987372 

•52 

38863i 

9-11 

611369 

i5 

46 

876519 

8*5 9 

987341 

•52 

389178 

9*io 

610822 

14 

47 

48 

377035 

8*58 

987310 

• 52 

389724 

9*oo 

610276 

i3 

377549 

8*57 

987279 

•52 

390270 

9*08 

609780 

12 

49 

378068 

8*56 

987248 

*52 

890816 

9*07 

609 1 85 
608640 

11 

5o 

378677 

8*54 

987217 

•52 

891360 

9* 06 

10 

5i 

9*310089 

8*53 

9.987186 

•52 

9*391903 

9*o5 

10*608097 

0 

52 

379601 

8*52 

987 I 55 

•52 

392447 

9*04 

607558 

8 

53 

38oi13 

8 * 51 

987124 

•52 

392989 

9*o3 

607011 

7 

54 

380624 

8*5o 

987092 

•52 

3g353 1 

9*02 

606469 

6 

55 

38 x1 34 

8*49 

987061 

•52 

394073 

9*01 

605927 

5 

54 

38 i 643 

8-4B 

987030 

•52 

394614 

o* oo 

6o53S6 

4 

5 ! 

382182 

8*47 

986998 

•52 

3g5154 

8.99 

604846 

3 

58 

382661 

8*46 

986967 

•52 

395694 

8*98 

604306 

2 

59 

383168 

8*45 

986936 

•52 

396263 

8-97 

603767 

1 

60 

383675 

8*44 

986904 

•52 

396771 

8*96 

603229 

0 

Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. 


26 (76 DEGREES.) 



































32 (14 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sir.e 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9*383675 

8.44 

9*986904 

•52 

9.396771 

8*96 

10*603229 

60 

i 

384182 

8*43 

986873 

• 53 

897809 

8*96 

602691 

5q 

2 

384687 

8*42 

986S41 

•53 

397846 

8* 9 5 

602164 

58 

3 

386192 

8* 41 

986809 

*53 

3 9 8383 

8*94 

601617 

5 ? 

4 

3856 9 7 

8-40 

986778 

*53 

398919 

8*93 

601081 

56 

5 

386201 

8 * 3 9 

986746 

• 53 

399455 

8*92 

6 oo 545 

55 

6 

386704 

8*38 

986714 

• 53 

399990 

8*91 

600010 

54 

7 

387207 

8 * 3 7 

986683 

• 53 

4oo524 

8*90 

599476 

53 

8 

387709 

8*36 

986651 

*53 

4oio58 

8*89 

598942 

52 

9 

388210 

8*35 

986619 

• 53 

401591 

8*88 

598409 

5 i 

IO 

388711 

8*34 

986587 

• 53 

402124 

8*87 

597876 

5 o 

11 

9*389211 

8*33 

9*986555 

*53 

9 * 402656 , 

8*86 

10*597344 

46 

I 2 

389711 

8*32 

986528 

*53 

403187 

8*85 

696813 

48 

i 3 

390210 

8 • 3 1 

986491 

*53 

403718 

8*84 

596282 

4 7 

14 

390708 

8 * 3 o 

986459 

*53 

404249 

8*83 

595761 

46 

i 5 

391206 

8*28 

986427 

*53 

404778 

8*82 

696222 

45 

16 

391703 

8*27 

986896 

*53 

4 o 53 o 8 

8 • 81 

694692 

44 

17 

392199 

8*26 

986363 

•54 

4o5836 

8* 80 

594164 

43 

18 

392690 

8*25 

98633i 

•54 

4o6364 

8*70 

5 g 3636 

42 

«9 

393191 

8*24 

986299 

• 54 

406892 

8*78 

593108 

41 

20 

3 9 3685 

8*23 

986266 

•54 

407419 

8*77 

592681 

40 

21 

9*394179 

8*22 

9*986234 

•54 

9*407945 

8*76 

10*592055 

3 9 

22 

394675 

8*21 

986202 

• 54 

408471 

8*75 

691529 

38 

23 

3 9 5 166 

8*20 

986169 

•54 

408997 

8*74 

691oo 3 

3 7 

24 

3 9 5658 

8*19 

986137 

• 54 

40902i 

8*74 

590479 

36 

25 

396150 

8-18 

986104 

*54 

4ioo45 

8* 7 3 

589966 

35 

26 

396641 

8*17 

986072 

•54 

410569 

8*72 

589431 

34 

2 7 

397132 

8*17 

986039 

•54 

411092 

8*71 

588 9 o8 

33 

28 

397621 

8* 16 

986007 

•54 

41161 5 

8*70 

588385 

32 

29 

398111 

8 • 1 5 

985974 

•54 

412137 

8*69 

587863 

3 i 

3 o 

398600 

8*14 

986942 

•54 

412668 

8*68 

587342 

3 o 

3 i 

9*399088 

8 • 1 3 

9•985909 

*55 

9• 4 i 3 179 

8*67 

io*58682i 

29 

32 

399576 

8*12 

985876 

• 55 

413699 

8*66 

5863 oi 

28 

33 

400062 

8*n 

985843 

• 55 

414219 

8*65 

585 7 8i 

27 

34 

400649 

8*io 

986811 

• 55 

414738 

8*64 

585262 

26 

35 

4oio35 

8*09 

985778 

• 55 

415267 

8*64 

584743 

25 

36 

4oi52o 

8*o8 

986745 

• 55 

416776 

8*63 

584225 

24 

37 

4o2oo5 

8*07 

986712 

• 55 

416293 

8*62 

583707 

23 

38 

402489 

8* 06 

986679 

• 55 

416810 

8 • 61 

583190 

22 

3 9 

402972 

8 *o 5 

985646 

• 55 

417326 

8* 60 

582674 

21 

40 

403455 

8*04 

9856i3 

• 55 

417842 

8 * 5 9 

582158 

20 

4 1 

9 * 4 o 3938 

8 *o 3 

9*98558o 

• 55 

9*4i8358 

8*58 

10*581642 

! 9 

42 

404420 

8*02 

985547 

• 55 

418873 

8*57 

581127 

18 

43 

404901 

8*oi 

9855i4 

• 55 

419387 

8*56 

58 o 6 i 3 

*7 

44 

406382 

8*oo 

985480 

• 55 

419901 

8*55 

580099 

16 

45 

4o5862 

7-99 

985447 

• 55 

42041 5 

8*55 

579585 

i 5 

46 

4o634i 

7.98 

985414 

• 56 

420927 

8*54 

579073 

i 4 

47 

406820 

7-97 

985380 

• 56 

421440 

8*53 

678:60 

i 3 

48 

407299 

7*96 

985347 

• 56 

421962 

8*52 

678048 

11 

49 

407777 

7.95 

985314 

•56 

422463 

8 * 5 i 

577537 

11 

5 o 

408264 

7-94 

986280 

• 56 

422974 

8 * 5 o 

577026 

10 

5 i 

9*408731 

7-94 

9*985247 

• 56 

Q * 423484 

8*49 

10*576516 

9 

5 s 

409207 

7* 9 3 

986213 

•56 

423993 

8*48 

576007 

8 

53 

409682 

7.92 

985180 

•56 

4245o3 

8 • 48 

575497 

7 

54 

410157 

7.9 1 

985146 

•56 

425oii 

8*47 

574989 

6 

55 

4io632 

7*90 

9861i 3 

• 56 

4255iq 

8*46 

57448i 

5 

56 

4m 06 

7 * 89 

980079 

•56 

426027 

8*45 

573973 

4 

57 

411579 

7*88 

985045 

• 56 

426534 

8*44 

573466 

3 

58 

412062 

I'll 

986011 

• 56 

427041 

8*43 

572950 

2 

59 

412524 

7*86 

984978 

• 56 

427547 

8*43 

672453 

1 

60 

412996 

7 -85 

984944 

• 56 

428062 

8*42 

571948 

0 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. 


(75 DEGREES.) 












































SINES AND TANGENTS. (15 DEGREES.) 33 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9412996 

7 - 

85 

9-984944 

* 5 7 

9-428052 

8.42 

10-571948 

60 

i 

413467 

7 

84 

984910 

.57 

428557 

8.41 

571443 

5 q 

2 

413938 

7 

83 

984876 

•57 

429062 

8-40 

570988 

53 

3 

414408 

7 

83 

984842 

•57 

429 566 

8 - 3 u 

070434 

5 ] 

4 

414878 

7 

82 

984808 

* 5 7 

430070 

8-38 

569930 

56 

5 

4 i 5347 

7 

81 

984774 

•57 

43 o 573 

8-38 

569427 

55 

6 

41 58 1 5 

7 

80 

984740 

* 5 7 

431075 

S’ 3 ? 

568 9 25 

54 

7 

416283 

7 

79 

984706 

•57 

431677 

3-36 

568423 

53 

8 

416761 

7 

78 

984672 

* 5 7 

432079 

8-35 

567921 

52 

9 

417217 

7 

77 

984637 

•57 

43258 o 

8-34 

567420 

5 i 

IO 

417684 

7 

76 

984603 

* 5 7 

433 o 8 o 

8-33 

566920 

5 o 

ii 

9 * 4 i 8 i 5 o 

7 

75 

9-984569 

* 5 7 

9 - 43358 o 

8-32 

10-566420 

49 

1 2 

41861 5 

7 

74 

984535 

*67 

434080 

8-32 

565 9 20 

48 

»3 

419079 

7 

73 

984500 

•57 

434579 

8 • 3 1 

565421 

47 

14 

419^44 

7 

73 

984466 

* 5 7 

435078 

8 - 3 o 

664922 

46 

i 5 

420007 

7 

72 

984482 

• 58 

435576 

8-29 

564424 

45 

16 

420470 

7 

7 i 

984397 

• 58 

436073 

8-28 

563 9 27 

44 

*7 

42oo33 

7 

70 

Q 84363 

• 58 

436570 

8-28 

56343 o 

43 

18 

421395 

7 

69 

984328 

• 58 

437067 

8-27 

562933 

42 

19 

421807 

7 

68 

984294 

• 58 

437563 

8-26 

562437 

4 i 

20 

422318 

7 

67 

984259 

• 58 

438 o 5 9 

8-25 

661941 

4 o 

21 

9-422778 

7 

6 7 

9-984224 

• 58 

9-438554 

8-24 

io- 56 i 446 

39 

22 

423238 

7 

66 

984IQO 

• 58 

439048 

8-23 

56 o 9 52 

38 

23 

423697 

7 

65 

984 l 55 

• 58 

439543 

8-23 

56 o 457 

37 

24 

424106 

7 

64 

984120 

• 58 

44 oo 36 

8-22 

55 99 64 

36 

25 

4246 i 5 

7 

63 

984085 

• 58 

44 o 52 9 

8-21 

559471 

35 

26 

425073 

7 

62 

984060 

• 58 

441022 

8-20 

558978 

34 

27 

42553o 

7 

61 

984015 

• 58 

44 i 5 i 4 

o‘ 19 

558486 

33 

28 

425987 

7 

60 

983981 

• 58 

442006 

8-19 

557994 

32 

o 9 


7 

60 

983946 

• 58 

442497 

8-18 

55 ~ i 5 o 3 

3 i 

3 o 

426899 

7 

5 9 

983911 

• 58 

442988 

8-17 

557012 

3 o 

3 i 

9-427354 

7 

58 

9-983875 

• 58 

9-443479 

8* 16 

io- 55652 i 

29 

32 

427809 

7 

57 

Q 83840 

• 5 9 

443968 

8* 16 

556 o 32 

28 

33 

428263 

7 

56 

9 838 o 5 

• 5 9 

444458 

8 • 1 5 

555542 

27 

34 

428717 

7 

55 

983770 

• 5 9 

444947 

8-14 

555 o 53 

26 

35 

429170 

7 

54 

983735 

• 5 9 

445435 

8- j 3 

554565 

25 

36 

429623 

7 

53 

983700 

• 5 9 

445923 

8-1 2 

554077 

24 

37 

430075 

7 

52 

983664 

• 5 9 

446411 

8-12 

553589 

23 

38 

430627 

7 

52 

983629 

• 5 9 

446898 

8-11 

553 io 2 

22 

39 

430978 

7 

5 i 

983594 

• 5 9 

447384 

8-io 

5526 i 6 

21 

40 

431429 

7 

5 o 

983553 

• 5 9 

447870 

8-09 

552 i 3 o 

20 

4 i 

9-431879 

7 

49 

9-983623 

• 5 9 

9*448356 

8-09 

10- 55 1644 

IQ 

42 

432329 

7 

49 

983487 

• 5 9 

448841 

8-08 

55 1159 

l8 

43 

432778 

7 

48 

983452 

• 5 9 

449326 

8-07 

550674 

17 

44 

433226 

7 

47 

983416 

• 5 9 

449810 

8-06 

55 oi 9 o 

l6 

45 

433675 

7 

46 

g 8338 i 

• 5 9 

45o2 9 4 

8-06 

549706 

i 5 

46 

434122 

7 

45 

983345 

• 5 9 

430777 

8 -o 5 

540223 

14 

47 

434569 

7 

44 

983309 

• 5 9 

461260 

8-04 

548740 

i 3 

48 

435 oi 6 

7 

44 

983273 

• 60 

461743 

8 -o 3 

548267 

12 

49 

435462 

7 

43 

9 83238 

• 60 

452225 

8-02 

54777 3 

11 

5 o 

435908 

7 

42 

983202 

•60 

452706 

8-02 

547294 

10 

5 i 

9*436353 

7 

4 i 

9 • 983166 

• 60 

9-453187 

8-oi 

io- 5468 i 3 

9 

52 

436798 

7 

40 

9831 3 o 

• 60 

453668 

8-oo 

546332 

8 

53 

437242 

7 

40 

983094 

•60 

454148 

7-99 

545852 

7 

54 

437686 

7 

3 9 

983008 

• 60 

454628 

7-99 

545372 

6 

55 

438129 

7 

38 

983022 

• 60 

456107 

7.98 

544898 

5 

56 

438672 

7 

37 

982986 

• 60 

455586 

7-97 

544414 

4 

57 

439014 

7 

36 

982960 

• 60 

406064 

7.96 

543 9 36 

3 

58 

439456 

7 

36 

982914 

• 60 

456542 

7.96 

543458 

2 

59 

439897 

7 

35 

982878 

• 6o 

457019 

7-96 

542981 

1 

60 

44 o 338 

7 

34 

982842 

• 60 

467496 

7.94 

542004 

0 

1 _ 

Cosine 

D. 

Sino 


Cotang. 

D. 

Tang. 

M. 


(74 DEGREES.) 















































34 (10 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

• " 

o 

9•44 o 338 

7-34 

9-982842 

• 60 

9-457496 

7-94 

io-542604 

60 

i 

440778 

7-33 

982805 

• 60 

457973 

7- 9 3 

542027 

5 q 

2 

441218 

7-32 

982769 

• 61 

458449 

7- 9 3 

541551 

58 

3 

44i658 

7 * 31 

982733 

• 61 

468920 

7-92 

641075 

57 

4 

442096 

7 * 31 

Q82696 

• 61 

459400 

7.91 

540600 

56 

J 

442535 

7-3 o 

982660 

•61 

459875 

7.90 

540125 

55 

6 

442973 

7-29 

982624 

•61 

460349 

7-9° 

539661 

54 

m 

I 

443410 

7-28 

982687 

•61 

460823 

7-89 

539177 

53 

8 

443847 

7-27 

982551 

•61 

461297 

7-88 

538703 

52 

9 

444284 

7-27 

982514 

•61 

461770 

7-88 

53823o 

5i 

10 

444720 

7-26 

982477 

•61 

462242 

7-87 

537758 

5o 

11 

9-445155 

7-25 

9-982441 

• 61 

9-462714 

7*86 

10-537286 

49 

1 2 

445590 

7-24 

982404 

•61 

463186 

7-85 

5368i4 

48 

i3 

446025 

7 -23 

982367 

•61 

463658 

7-85 

536342 

47 

14 

446459 

7-23 

982331 

•61 

464129 

7-84 

535871 

46 

i5 

446893 

7*22 

982294 

•61 

464699 

7-83 

5354oi 

45 

16 

447326 

7-21 

982257 

•61 

465069 

7 - 83 

53493 i 

44 

*7 

447759 

7-20 

982220 

• 62 

465539 

7-82 

534461 

43 

18 

448191 

7 • 20 

982183 

•62 

466008 

7-81 

533992 

42 

«9 

448623 

7 * 1 9 

982146 

• 62 

466476 

7-80 

533024 

4i 

20 

449054 

7.18 

982109 

•62 

466945 

7-80 

533o55 

4o 

21 

9-449485 

7*i7 

9-982072 

•62 

9-467413 

7-79 

10-532587 

3 9 

22 

449915 

7* 16 

982035 

•62 

467880 

7.78 

532120 

38 

23 

45 o 345 

7’ 16 

981998 

•62 

468347 

7.78 

531653 

3 7 

24 

450776 

7’ i5 

981961 

•62 

468814 

I’ll 

531186 

36 

25 

45i2o4 

7 -i 4 

981924 

•62 

469280 

7-76 

530720 

35 

26 

45 i 632 

7‘ l3 

981886 

•62 

469746 

7- 7 5 

53o254 

34 

27 

452 o 6 o 

7 * 1 3 

981849 

•62 

470211 

7.70 

529789 

33 

28 

452488 

7.12 

981812 

•62 

470676 

7-74 

529324 

32 

29 

452915 

7.h 

981774 

•62 

471141 

7-73 

528869 

3i 

3o 

453342 

7’ 10 

981737 

•62 

471606 

7- 7 3 

528390 

3o 

3r 

9-453768 

7’ 10 

9-981699 

•63 

9-472068 

7.72 

10-527932 

29 

32 

454194 

7'°9 

981662 

•63 

472532 

7.71 

527468 

28 

33 

454619 

7-08 

981625 

•63 

472995 

7-71 

527005 

27 

34 

455 o 44 

7-07 

981687 

•63 

473407 

7.70 

526543 

26 

35 

455469 

7-07 

981549 

•63 

473919 

7-69 

526081 

25 

36 

455893 

7 ’o6 

981512 

•63 

47438 i 

7.69 

5256iq 

24 

3 7 

456316 

7 ’o5 

981474 

•63 

474842 

7-68 

525158 

23 

38 

466739 

7-04 

981436 

•63 

4753o3 

7.67 

524697 

22 

3 9 

457162 

7-04 

981399 

•63 

475763 

7-67 

524237 

21 

4o 

457584 

7 ’o3 

981361 

•63 

476223 

7-66 

523777 

20 

4i 

9-458oo6 

7’02 

9-981323 

•63 

9-476683 

7-65 

io-5233i7 

19 

42 

458427 

7 -01 

981285 

•63 

477>42 

7-65 

522858 

lb 

43 

458848 

7’0i 

981247 

•63 

477601 

7-64 

522399 

17 

44 

459268 

7-00 

981209 

•63 

478059 

7-63 

521941 

l6 

45 

459688 

6-90 

981171 

•63 

478517 

7-63 

521483 

i5 

46 

460108 

6-98 

981133 

•64 

478975 

7-62 

521025 

14 

47 

460627 

6-98 

981095 

•64 

479432 

7-61 

520568 

13 

48 

460946 

6-97 

981067 

•64 

479889 

7-61 

520111 

12 

49 

461364 

6-96 

981019 

•64 

480340 

7-60 

5 i 9655 

11 

5o 

461782 

6-96 

980981 

•64 

480801 

7-5 9 

519199 

10 

5 i 

9-462199 

6-96 

9-980942 

• 64 

9-481257 

7-59 

10 • 518743 

Q 

52 

462616 

6-94 

980904 

•64 

481712 

7-58 

518288 

§ 

53 

463o32 

6-93 

980866 

•64 

482167 

7- 5 7 

517833 

7 

54 

463448 

6-93 

980827 

•64 

482621 

7- 5 7 

517379 

6 

55 

463864 

6-92 

980789 

•64 

483075 

7-56 

516925 

5 

56 

464279 

6-91 

980760 

•64 

483529 

7 • 55 

516471 

4 

67 

464694 

6-90 

980712 

•64 

483982 

7-55 

5i6oi8 

0 

58 

465 1 08 

6-90 

980673 

• 64 

484435 

7-54 

5i5565 

2 

59 

465522 

6*89 

980635 

•64 

484887 

7-53 

5i5ii3 

1 

60 

466935 

6’88 

980596 

•64 

48533 9 

7-53 

5 i 466 i 

0 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. 


(73 DEGREES.) 














































SINES AND TANGENTS. - (17 DEGREES.) : 85 


M. 


Sine 

D. 

Cosine 

1>. 


Tang. 

I). 

Cotang. 


o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

IO 

u 

13 

u 

15 

16 

‘7 

18 

'9 

20 

2 l 
22 

23 

24 

25 

26 

2 7 

28 

30 

31 

32 

33 

34 

35 

36 

& 

39 

40 

4t 

42 

43 

44 

45 

46 

47 

48 

i 9 

5r 

52 

53 

54 

55 

56 

u 

u 

< 

9-465935 

466348 

466761 

467173 

467685 

467996 

468407 

468817 

469227 

469637 

470046 

9-470455 

470863 
471271 
471679 
472086 
472492 
472898 
4733o4 
473710 
474 i x5 

9-4745i9 

474923 

475327 

475730 

476133 

476536 

476938 

477340 

477741 

478142 

9-478542 
478942 
479342 
479741 
480140 
480539 
480987 
48t334 
481731 
482128 

9-482525 

482921 

483316 

483712 

484107 

4845 oi 

484896 

485289 

486682 

486075 

9.486467 

486860 

487251 

487643 

488o34 

488424 

488814 

489204 

489693 

489982 

6-88 

6-83 

6-87 

6-86 

6-85 

6-85 

6-84 

6-83 

6-83 

6-82 

6*81 

6-80 

6-80 
6-79 
6-78 
6-78 
6-77 
6-76 
6-76 
6-75 
6-74 

6-74 

6- 7 3 

6-72 

6-72 

6-71 

6-70 

6-69 

6-69 

6-68 

6-67 

6-67 

6«66 

6-65 

6-65 

6-64 

6-63 

6-63 

6-62 

6-61 

6 • 61 

6-60 
6-5 9 

6-5 9 
6-58 
6-5 7 
6-57 
6-56 
6-55 
6-55 
6-54 

6-53 

6-53 

6-52 

6 * 51 
6-5r 
6-5o 
6-5o 
6-49 
6-48 
6-48 

9-980696 

980538 

980519 

980480 

980442 

980403 

980364 

98o325 

980286 

980247 

980208 

9-980169 

980130 

980091 

980032 

980012 

979973 

979934 

979896 

979836 

979816 

9-979776 

979707 

979697 

979668 

979618 

979579 

979539 

979499 

979459 

979420 

9-979380 

979340 

979300 

979260 

979220 

979180 

979140 

979100 

979059 

979019 

9-978979 

978939 

978898 

978808 

978817 

978777 

978736 

978696 

978606 

978615 

9-978674 

978533 

9784 q 3 

978452 

978411 

978370 

978329 

978288 

978247 

978206 

.64 

.64 

■65 

-65 

-65 

•65 

•65 

•65 

-65 

-65 

•65 

-65 

-65 

-65 

• 65 
■ 65 

• 65 
-66 

• 66 
-66 
• 66 

-66 
-66 
• 66 
-66 
-66 
• 66 
• 66 
•66 
•66 
• 66 

• 66 
-66 
.67 
.67 

•67 

•67 

•67 

•67 

•67 

• 67 

•67 

•67 

.67 

.67 

.67 

•67 

•67 

• 68 
• 68 
• 68 

• 68 
• 68 
• 68 
• 68 
• 68 
• 68 
-68 
• 68 
• 68 
• 68 

< 

9*485339 

485791 

486242 

486693 

487143 

487598 

488043 

488492 

488941 

489390 

489838 

9-490286 

490733 

491180 

491627 

492073 

492519 

492960 

493410 

498854 

494299 

9-494743 

496186 

49363o 

496073 

496616 

496957 

497399 

497841 

498282 

498722 

9-499163 

499603 

600042 

5 oo 48 i 

600920 

5 oi 359 

501797 

5 o 2235 

002672 

5 o 3 io 9 

9-5 o 3546 
503982 
5 o 44 i 8 
5 o 4854 
505289 
605724 
606159 
5o6593 
507027 
507460 

9-507893 
5o83 26 
608739 
609191 
609622 

5 1oo 54 

5 1o 485 
610916 
5 h 346 
611776 

7*55 

702 

7- 5r 
j*5i 
7-5 o 
7*49 
7-49 
7-48 

7-47 

7-47 

7-46 

7-46 

7.45 

7*44 

7-44 

7*43 

7*43 

7.42 

7.41 

7*40 

7-40 

7.40 

7- 3 9 

7-38 

7.37 

7-37 

7-36 

7*36 

7.35 

7-34 

7-34 

7-33 

7-33 

7-32 

7*3' 

7-3r 

7 • 3o 

7-3o 

7.20; 

7-28 

7-28 

7-27 

7.27 

7-26 

7-253 

7-26 

7-24 

7-24 

7-23 

7-22 

7-22 

7-21 

7-2r 

7-20 

7-19 

;:!? 

7-18 

7**7 

7-16 

7-16 

io- 5 i 466 i 

614209 

5 i 3753 

5 1 3307 
512857 ' 
512407 

5i1957 

5ii5o8 

5i1069 
5io6io 
610162 

10*509714 

509267 

500820 

5o8373 

507927 

507481 

5o7o35 

506590 

5o6i46 

600701 

io- 5 o 5257 

5 o 48 i 4 

504370 

603927 

5o3485 

5 o 3 o 43 

602601 

5o2i5o 

601718 

601278 

io* 5 oo 837 
500397 
499958 
499619 
499080 
498641 
498203 
497766 
497328 
496891 

0 • 496454 

496018 
496682 
496146 
494711 
494276 
493841 
493407 
492973 
492340 

0-492107 

491674 

491241 

490809 

490378 

489946 

489615 

489084 

488664 

488224 

60 

57 

56 

55 

64 

53 

52 

5i 

5o 

40 

48 

47 

46 

45 

44 

43 

42 

41 
4o 

39 

38 

3? 

36 

35 

34 

33 

32 

3i 

3o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

10 

IO 

17 

l6 

i5 

i4 

i3 

12 

n 

10 

7 

6 

5 

4 

3 

2 

i< ,; 

0 


Cosine j 

D. 

Sine 

D. 

Cotarig. [ 

D. 

Tans*. 

M.V. 


17 (72 DEGREES.) 























































36 (18 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

0-489982 

6 • 48 

9-978206 

-68 

9-511776 

7.16 

10-488224 

60 

i 

490371 

6-48 

978165 

-68 

512206 

7.16 

487794 

-2 

2 

490769 

6-47 

978124 

• 68 

512635 

7 * 15 

487663 

38 

3 

4 

491U7 

49i535 

6-46 

6-46 

978083 

978042 

•69 

-69 

5 i 3 o 64 

5 i 3493 

7-U 

7-14 

486936 

486607 

57 

56 

5 

491922 

492308 

6-45 

978001 

•69 

5i3o2i 

7 -13 

486079 

55 

6 

6-44 

977969 

977918 

977877 

•69 

514649 

7 *i 3 

48565 i 

54 

l 

492695 

493081 

6-44 

6-43 

•69 

•69 

514777 

5 i 52 o 4 

7-12 

7-12 

485223 

484796 

53 

52 

*> 

493466 

6-42 

977835 

•69 

5 i 563 i 

7-u 

484669 

5i 

IC 

49385 i 

6-42 

977794 

•69 

516067 

7-10 

486946 

5o 

i i 

9-494236 

6-4 i 

9.977752 

-69 

9*516484 

7-10 

io- 4835 i 6 

4o 

12 

i3 

494621 

496005 

6-41 

6-40 

977711 
977669 

•69 

-69 

516910 

5n635 

7-09 

7.09 

483090 

482665 

48 

47 

14 

495388 

6-39 

977628 

•69 

517761 

7-08 

482239 

46 

i5 

495772 

6-39 

977686 

•69 

518185 

7-oS 

481810 

45 

16 

496154 

6-38 

977544 

•70 

518610 

7-07 

481390 

44 

17 

496537 

6-37 

9775 o 3 

.70 

519034 

7-06 

480966 

43 

18 

496919 

497001 

6*37 

97746 i 

.70 

519438 

7-06 

480342 

42 

19 

6-36 

977419 

• 70 

519882 

7 -o 5 

480118 

4i 

20 

497682 

6-36 

977377 

.70 

52 o 3 o 5 

7-03 

479695 

40 

21 

9•498064 

6-35 

9-977335 

.70 

9-520728 

7-04 

10-479272 

478849 

? 9 

22 

498444 

6-34 

977293 

.70 

521151 

7-o3 

38 

23 

498825 

6-34 

977251 

.70 

521573 

7 -o 3 

478427 

37 

24 

499204 

6-33 

977209 

• 70 

521995 

7 -o 3 

478005 

36 

23 

499684 

6-32 

977167 

.70 

522417 

7-02 

477583 

35 

26 

499963 

6-32 

977125 

• 70 

522838 

7-02 

477162 

34 

27 

5oo342 

6 • 31 

977083 

.70 

523 2 5 9 

7-01 

476741 

33 

28 

600721 

6 • 31 

977041 

.70 

52368o 

7-oi 

476620 

32 

29 

501099 

6-3o 

976999 

.70 

524100 

7-oo 

475900 

3i 

3o 

601476 

6-29 

976907 

.70 

524620 

6.99 

475480 

3o 

3i 

9-5 oi 854 

6-29 

9.976914 

976872 

.70 

9-524939 

6-Q9 

10-475061 

29 

32 

5 o 223 i 

6*28 

•7i 

525659 

526778 

6.9S 

474641 

28 

33 

602607 

6-28 

976860 

•7i 

6.98 

474222 

2 7 

34 

502984 

5o336o 

6-27 

976787 

•7i 

526197 

6.97 

4738 o 3 

26 

35 

6-26 

976745 

•7i 

5266 i 5 

6-97 

473385 

23 

36 

5 o 3735 

6-26 

976702 

•7i 

527033 

6.96 

472967 

472349 

24 

37 

5 o 4 i10 

6-25 

976660 

•7i 

527461 

6-96 

23 

38 

5 o 4485 

6-25 

976617 

•71 

527868 

6. 9 5 

472132 

22 

3g 

5 o 486 o 

6-24 

976574 

•7i 

528286 

6- 9 5 

4717*5 

2 I 

4o 

5 o 5234 

6-23 

976562 

•7i 

528702 

6.94 

471298 

20 

41 

9*5 o 56 o 8 

6-23 

9-976489 

•7i 

9-529119 

6. ,3 

10-470881 

IO 

42 

505981 

6-22 

976446 

•7i 

529533 

6. 9 3 

470465 

l8 

43 

5 o 6354 

6-22 

976404 

•7i 

529960 

53o366 

6-98 

470060 

17 

44 

506727 

6-21 

976661 

•7i 

6.92 

46 o 634 

16 

45 

607099 

6-20 

676318 

•71 

530781 

6-91 

469219 

i5 

46 

507471 

6-20 

976275 

.71 

531196 

6.91 

468804 

14 

47 

507843 

6-19 

976262 

•72 

53 i 6 i1 

6.90 

46838a 

i3 

48 

5o82i4 

6* 10 

976189 

•72 

532025 

6.90 

467976 

467661 

12 

49 

5o8585 

6-18 

976146 

•72 

532439 

532856 

6-89 

11 

5c 

508956 

6-18 

976103 

.72 

6.89 

467147 

iO 

5i 

9.509326 

6-17 

9-976060 

.72 

9-533266 

6-88 

10-466734 

9 

52 

509696 

6-16 

976017 

•72 

533679 

6-88 

466621 

8 

53 

5ioo65 

6-16 

975974 

.72 

534092 

6-87 

465908 

7 

54 

510434 

6-15 

976930 

975887 

.72 

5345o4 

6-87 

4654 q 6 

w# 

55 

5io8o3 

6 • 15 

.72 

534916 

6-86 

465o84 

5 

56 

5i1172 

6-14 

975844 

•72 

535328 

6-86 

464672 

4 

57 

5 ii 54 o 

6-13 

975800 

•72 

535739 

6-85 

464261 

} 

58 

511907 

6-13 

975757 

*72 

53615o 

6-85 

46385o 


69 

512276 

6-12 

975714 

.72 

53656i 

6-84 

463439 

463 o 2 o 

1 

60 

512642 

6-12 

976670 

.72 

536972 

684 

c 


Cosino 

D. 

Sine 

D. 

Cotang. 

D. 

1 »ng. 

i m. 


(71 DEGREES.) 

















































SINES AND TANGENTS. (19 DEGREES.) 


37 


M. 

Sine 

D. 

Cosine 

D. 

J Tang. 

D. 

Cotang. 

" 

0 

9*512642 

6* 12 

9*975670 

•78 

9*536972 

6*84 

10*463028 

60 

i 

513009 

6*u 

970627 

•78 

53 7 382 

6*83 

462618 

5 q 

s 

§13370 

6*ii 

970583 

•78 

537792 

6*83 

462208 

58 

3 

518741 

6*io 

970039 

•78 

538202 

6*82 

461798 

5 7 

4 

514107 

6*09 

970496 

•78 

5386i1 

6*82 

461M9 

56 

5 

5(4472 

6* 09 

975402 

•78 

539020 

6 • 81 

460980 

55 

6 

514837 

6* 08 

975408 

•78 

539429 

6 • 81 

460071 

54 

7 

5l0202 

6* 08 

975365 

•78 

539837 

6* 80 

460163 

53 

8 

515566 

6*07 

975321 

* 7 3 

540245 

6* 80 

409755 

02 

9 

5i5g3o 

6.07 

975277 

•78 

54o653 

6*79 

40934.7 

5i 

IO 

616294 

6*o6 

970233 

•78 

541061 

6*79 

408939 

5o 

ii 

9 * 516667 

6*o5 

9.975189 

•78 

9*541468 

6*78 

io*4o8532 

4 q 

12 

517020 

6*o5 

970140 

*73 

541875 

6*78 

458i25 

48 

i3 

517382 

6*04 

970101 

.73 

542281 

6*77 

457719 

47 

14 

517745 

6*04 

970057 

•78 

542688 

6*77 

45 7 312 

46 

i5 

518107 

6*o3 

975oi3 

*73 

543094 

6*76 

436906 

45 

16 

518468 

6*o3 

974969 

•74 

543499 

6*76 

4565oi 

44 

1 l l 

518829 

6*02 

974920 

•74 

543905 

6*70 

406095 

43 

18 

519190 

6*oi 

974880 

•74 

5443IO 

6*70 

4556oo 

42 

19 

519601 

6*oi 

974836 

•74 

544710 

6*74 

455285 

4i 

20 

519911 

6*oo 

974792 

•74 

540119 

6-74 

45488i 

4o 

21 

9*520271 

6*oo 

9*974748 

•74 

9 045524 

6*73 

10*404476 

3g 

22 

52o63i 

5*99 

974703 

•74 

540928 

6*73 

464072 

38 

23 

520990 

5*99 

974609 

•74 

546331 

6*72 

453669 

37 

24 

521349 

5*98 

974614 

•74 

546735 

6*72 

453265 

36 

25 

521707 

5.98 

974570 

*74 

547138 

6*71 

462862 

35 

26 

522066 

5*97 

974020 

•74 

547540 

6*71 

462460 

34 

27 

522424 

5*96 

97448i 

•74 

547943 

6*70 

432057 

33 

28 

522781 

5*96 

974436 

•74 

548345 

6*70 

45i655 

32 

29 

5a3 38 

5* 9 5 

974391 

•74 

548747 

6*69 

431253 

3i 

3o 

5234g5 

5*95 

974347 

*70 

549149 

6*69 

45o85i 

3o 

3i 

9*523852 

5*94 

9*9743o2 

• 75 

9*54955o 

6*68 

io*4oo45o 

29 

32 

524208 

5*94 

974207 

.75 

549951 

6*68 

430049 

28 

33 

524564 

5*93 

974212 

•75 

55o302 

6*67 

449648 

27 

34 

624920 

5*93 

974167 

.75 

55o752 

6*67 

449248 

26 

35 

520276 

5*92 

974122 

.75 

551152 

6*66 

448848 

25 

36 

52563o 

5*91 

974077 

*?5 

55i002 

6*66 

448448 

24 

3 7 

520984 

5* 9 i 

974o32 

•75 

55i952 

6*65 

448048 

23 

38 

526339 

5*90 

973987 

.70 

5 5 2 3 51 

6*65 

447649 

22 

3 9 

526693 

5*90 

973942 

•7? 

552750 

6*65 

44 7 25o 

21 

40 

527046 

5*89 

973897 

* 7 5 

553i49 

6*64 

446851 

20 

41 

9*527400 

5*89 

9*973852 

•75 

9*553548 

6*64 

io*446452 

IQ 

42 

527753 

5*88 

973807 

•7? 

553946 

6*63 

446004 

10 

43 

528100 

5*88 

973761 

.70 

554344 

6*63 

445656 

17 

! 44 

528408 

5*8 7 

973716 

.76 

554741 

6*62 

445259 

l6 

45 

528810 

6*87 

973671 

.76 

555i3g 

6*62 

444861 

i5 

46 

529161 

5*86 

973625 

.76 

555536 

6*6i 

444464 

14 

47 

5295i3 

5*86 

9 7 358o 

.76 

555933 

6 • 61 

444067 

i3 

48 

529864 

5*85 

973535 

.76 

5o632g 

6* 60 

443671 

12 

: 49 

53o2i5 

5*85 

973489 

.76 

556725 

6* 60 

4432 7 5 

n 

5o 

53o565 

5*84 

978444 

.76 

557121 

6*59 

442879 

JO 

5i 

9•53og15 

5*84 

9*973398 

.76 

9*557617 

6*5 9 

10*442483 

9 

5a 

531265 

5*83 

973302 

•76 

507913 

6*5g 

442087 

8 

53 

531614 

5*8j 

973307 

.76 

5583o8 

6*58 

441692 

7 

54 

53io63 

5*82 

973261 

.76 

508702 

6*58 

441298 

6 

55 

532312 

5*8i 

9 7 32i5 

.76 

559097 

6*67 

440903 

5 

56 

53266 i 

5*8i 

973169 

.76 

559491 

6*5 7 

440009 

4 

57 

533009 

5* 80 

973124 

*76 

55 9 885 

6*56 

440110 

3 

58 

533357 

5*8o 

973078 

•76 

660279 

6*56 

439721 

2 

5 9 

533704 

5.70 

9 7 3o32 

•77 

560678 

6*55 

439327 

1 

60 

534 o 52 

5*78 

972986 

*77 

561066 

6*55 

438934 

0 

L 

CeSoi 

D. 

Sine 

D. 

Cotang. 

D. 

Tang, j M. 


(70 DEGREES.) 


























































(20 DEGREES.; A TABLE OF LOGARITHMIC 


38 


M. 

&Ine 

D. 

Cosine 

D. 

Tung. 

D. 

Cotang. 


o 

1 

2 

3 

4 

5 

6 

l 

9 

10 

11 

12 

1 3 

14 

15 

16 
; *7 
! 18 

»9 

20 

21 

22 

23 

24 

25 
i 26 

27 

28 

29 

3 0 

3 1 

32 

33 

34 

35 

36 

37 

38 

39 

40 

4 1 

42 

43 

44 

45 

46 

47 

48 

3 

5 1 

52 

53 

54 

55 

56 

:!!2 

2 

1 • a 

. 

9*534o5i 

534399 

534740 

536092 

535438 

535783 

536129 
536474 
5368 18 
537 i 63 
537507 

9*537851 

538194 

538538 

53888 o 

539223 

539565 

539907 

540249 

540590 

540931 

9*541272 
54161 3 
541953 
542293 
542632 
542971 
5433 10 
543649 
543 o 87 
544325 

9*544663 

540000 

545338 

540674 

546011 

546347 

546683 

547019 

547354 

547689 

9 • 548024 

548359 

548693 

549027 

54936 o 

549693 

550026 

55 o 359 

550692 

55 io 24 

9 * 55 i 356 

551687 

552018 

552349 

55268o 

553 oio 

553341 

553670 

554000 

554329 

5.78 

5*77 

5.77 

5.77 

5*76 

5.76 

5*75 

5*74 

5*74 

5*73 

5*73 

5.72 

5*72 

5*7i 

5*71 

5*70 

5*70 

6*69 

5*69 

5*68 

5*68 

5*67 

5*67 

5*66 

5*66 

5*65 

5*65 

5*64 

5*64 

5*63 

5*63 

5*62 

5*62 

5 * 6 i 

5 * 6 i 

5 * 60 
5 * 6 o 

5*59 

5*59 

5*58 

5*58 

5*57 

5*57 

5*56 

5*56 

5*55 

5*55 

5*54 

5*54 

5*53 

5*53 

5*52 

5*52 

5*52 

5 * 5 r 

5 * 5 i 

5 * 5 o 

5 * 5 o 

5.49 

5*49 

5*48 

9*972986 
972940 
972894 
972848 
972802 
972755 
972709 
97 2663 
972617 
972570 
972524 

9.972478 

97243 i 

972385 

972338 

972291 

972245 

972198 

972161 

972105 

972 o 58 

9*972011 

971964 

97*917 

97*870 

97*823 

971776 

971729 

971682 

97*635 

97*588 

9.971540 
971493 
971446 
97U98 
971 3 d 1 
97i3o3 
971256 
97i208 
971161 
97 Hi 3 

9*971066 

971018 

970970 

970922 

970874 

970827 

970779 

970781 

970683 

970635 

9 *970586 
970538 
970490 
970442 
970394 

970345 

970297 

970249 

970200 
970. D2 

•77 

•77 

•77 

•77 

•77 

77 

'77 

•77 

•77 

•77 

*77 

•77 

•78 

.78 

•78 

.78 

.78 

.78 

.78 

•78 

.78 

.78 

•78 

.78 

•7» 

•78 

.78 

•79 

•79 

•79 

•79 

•79 

•79 

•79 

•79 

•79 

•79 

•79 

*79 

•79 

*79 

• 80 
•80 

• 80 
.80 

• 80 

• 80 

• 8o 

• 80 

• 80 
•80 

•80 

• Bo 

• 80 

• 80 
•80 
•81 
•81 
•81 . 
•81. 
•81 

9*56io66 
661469 
56i85i 
662244 
562636 
563o28 
563419 
5638 11 
564202 
564092 
564983 

9.565373 

565763 

566 i 53 

566542 

566932 

567320 

567709 

568oo8 

568486 

568873 

9.569261 

569648 

570035 

570422 

570809 

571190 

571081 

571967 

572352 

572738 

9.573123 

573507 

573892 

574276 

574660 

570044 

570427 

572810 

576193 

676676 

9.576958 

577841 

577723 

678104 

578486 

578867 

679248 

579629 

58 oooo 

58o3S9 

9*580769 

581149 

58i528 

581907 

582286 

582665 

583o43 

583422 

5838 oo 

584177 

6*55 

6*54 

6-54 

6-53 

6-53 

6-53 

6*52 

6-52 

6 * 5 i 

6 * 5 i 

6 * 5 o 

6 - 5 o 

6-49 

6*49 

6*49 

6*48 

6.48 

6-47 

6*47 

6*46 

6*46 

6-45 

6-45 

6-45 

6-44 

6*44 

6-43 

6*43 

6*42 

6*42 

6-42 

641 

6-41 

6-40 

6*40 

6.39 

6*39 

6*39 

6-38 

6-38 

6*37 

6*37 

6-36 

6*36 

6*36 

6-35 

6*35 

6^34 

6*34 

6-34 

6*33 

6*33 
6*32 
6*32 
6 * 3 a 
6 * 3 i 
6 * 3 1 
6 * 3 o 
6 * 3 o 
6*29 
6*29 

10*438934 

438341 

408149 

437756 
437364 
436972 
43658i 
436189 
435798 
4354 o 8 
435oi 7 

10*484627 

434237 

433847 

433458 

433 o 68 

432680 

482291 

431902 

43 iDi 4 

431127 

10*430739 

43o352 

429965 

429378 

429191 

428805 

428419 

428o33 

427648 

427262 

10*426877 
42649 3 
426108 
426724 

425340 

424956 

424373 

424190 

423807 

423424 

io* 423 o 4 i 
422669 
422277 
421896 
421614 
4211 33 
42.1752 
42^871 

419991 
419611 

10*419231 

4i885i 

418472 

418093 

417714 

417335 

416967 

416078 

416200 

4 i 5823 

60 

5$ 

57 

56 

55 

54 

53 

5 a 

5i 

5 o 

49 

48 

47 

46 

4 > 

44 

43 

42 

4 i 

40 

$ 

3 ? 

36 

35 

34 

33 

32 

3 i 

3o 

28 

27 

26 

25 

24 

23 

22 

21 

20 

s 

i 5 

14 

i3 

12 

it 

10 

J 

1 

5 

4 

3 

2 

1 

0 

Cosine 

D. 

Siiie 

D. 

Cotang. 

3d 

- 

M. 


(69 DEGREES,) 





















































SINES AND TANGENTS. (21 DEGREES.) 39 


11. 

Sine 

D. 

Cosine 

D. 

Tung. 

D. 

Cotang. 


o 

9•554320 

5-48 

9"97 oi 52 

.81 

9.584177 

6*29 

io* 4 i 5823 

60 I 

1 

554658 

5.48 

970103 

• 81 

584555 

6*29 

5445 

5o 

2 

554987 

5-4? 

97 oo55 

• 81 

584 9 32 

6-28 

4 i 5 o 68 

58 

3 

555315 

5.47 

970006 

• 81 

5853o 9 

6-28 

414691 

57 

4 

555643 

5-46 

969957 

• 81 

585686 

6-27 

414314 

56 

5 

555971 

5.46 

969909 

• 8i 

586062 

6-27 

4i3 9 38 

55 

6 

556299 

5.45 

969860 

• 81 

086489 

6-27 

4 i 356 i 

54 

7 

556626 

5-45 

969811 

• 81 

5868i5 

6*26 

413185 

53 

8 

556 9 53 

5-44 

969762 

• 81 

587190 

6*26 

412810 

52 

9 

557280 

5-44 

969714 

• 81 

587566 

6-25 

412434 

5i 

so 

557606 

5.43 

969665 

• 81 

687941 

6-25 

4i2o5 9 

5o 

si 

Q.557932 

5.43 

9-969616 

.82 

9-588316 

6-25 

10-411684 

4o 

12 

558258 

5-43 

969667 

.82 

688691 

6-24 

41i 3 o 9 

48 

13 

558583 

5-42 

969518 

•82 

589066 

6*24 

410934 

47 

*4 

558909 

5-42 

969469 

• 82 

589440 

6-23 

410060 

46 s 

j 

55 q 234 

5-4i 

969420 

.82 

58 9 8i4 

6-23 

410186 

45 

*6 

55 9 558 

5-4i 

969370 

.82 

5 9 oi88 

6-23 

409812 

44 

| *7 

55 9 883 

5.40 

969321 

•82 

5 9 o562 

6-22 

409438 

43 

18 

560207 

5-40 

969272 

• 82 

690935 

6-22 

4 oqo 65 

42 

*9 

56o53i 

5-3 9 

969223 

.82 

591308 

6-22 

408692 

41 ! 

SO 

56o8§5 

5-3 9 

969173 

.82 

591681 

6*21 

4083!9 

40 | 

21 

9.561178 

5-38 

9-969124 

.82 

9.592054 

6*21 

JO-407946 

3 9 : 

22 

56i5oi 

5-38 

969075 

• 82 

592426 

6*20 

407O74 

38 : 

23 

561824 

5 • 37 

969025 

• 82 

592798 

6*20 

407202 

37 ; 

! 24 

562146 

5.3 7 

968976 

.82 

593170 

6* 19 

4o682 9 

36 

25 

562468 

5-36 

968926 

• 83 

5 9 3542 

6*19 

406458 

35 

26 

562790 

5-36 

968877 

• 83 

693914 

6* 18 

406086 

34 

a 7 

563 12 

5-36 

968827 

.83 

5 9 4285 

6-18 

4 o 5 7 i 5 

33 | 

28 

563433 

5.35 

968777 

.83 

5 9 4656 

6> 18 

405344 

32 • 

' *9 

563 7 55 

5-35 

968728 

• 83 

5 9 5o27 

6-17 

4 o 4 97 3 

3i 

2 o 

564075 

5-34 

968678 

• 83 

5 9 53 9 8 

6-17 

404602 

3° | 

2 i 

9 • 564396 

5.34 

9.968628 

• 83 

9.595768 

6*17 

io* 4 o 4232 

29 ] 

32 

564716 

5-33 

968678 

• 83 

696138 

6-16 

4o3862 

28 : 

33 

565o36 

5-33 

9 68528 

• 83 

596608 

6* 16 

408492 

27 

34 

565356 

5-32 

968479 

• 83 

696878 

6-16 

4o3l22 

26 

35 

5656 7 6 

5-32 

968429 

• 83 

697247 

6-15 

4 o 2 7 53 

25 

36 

566995 

5 - 31 

968379 

• 83 

597616 

6-15 

402384 

24 

S 7 

566314 

53i 

968829 

•83 

5 97 o85 

6-15 

4o2oi5 

23 | 

38 

566632 

5 • 3 * 

968278 

• 83 

598354 

6.14 

4o1646 

22 i 

3 9 

566961 

5-3o 

968228 

• 84 

5 9 8 7 22 

6-14 

401278 

21 | 

4o 

567269 

5-3o 

968178 

• 84 

099091 

6- i 3 

400909 

20 . 

4i 

9.567587 

5.29 

9-968128 

.84 

9.599459 

6 * 13 

10.400641 

*9 

; 42 

567904 

5*29 

968078 

.84 

599827 

6 • 13 

4 ooi 7 3 

18 ; 

43 

568222 

5-28 

968027 

.84 

600194 

6*12 

899806 

>7 

44 

56853 9 

5-28 

967977 

.84 

6 og 562 

6-12 

399438 

16 

45 

568856 

5-28 

967927 

.84 

600929 

6-11 

899071 

i5 

46 

569172 

5-27 

967876 

.84 

601295 

6* 11 

398704 

14 

47 

569488 

5*27 

967826 

.84 

601662 

6-11 

3 9 8338 

13 

48 

569804 

5- 26 

967775 

.84 

602029 

6- io 

397971 

12 

49 

570120 

5-26 

967726 

.84 

602890 

6*io 

3 97 6o5 

11 

5o 

5 7 o435 

5-25 

967674 

.84 

602761 

6-10 

3 97 23 9 

10 

5i 

9.570731 

5-25 

9-967624 

.84 

9-6o3i2 7 

6-09 

io.3 9 68 7 3 

2 i 

£2 

571066 

5-24 

967673 

.84 

6 o 3493 

6-09 

3 9 65o 7 

6 1 

53 

571380 

5-24 

967522 

.85 

6o3858 

6-09 

396142 

7 

54 

571696 

5-23 

967471 

.85 

604223 

6-o8 

395777 

6 j 

55 

572009 

5-23 

967421 

*85 

6o4588 

6-08 

395412 

5 i 

56 

572828 

5-23 

967870 

• 85 

6 o 4 q 53 

6-07 

896047 

4 

§7 

5 7 2636 

5-22 

9 6 7 3 iq 

• 85 

6 o 53 i 7 

6-07 

394688 

3 


5 7 2 9 5 o 

5*22 

967268 

• 85 

6 o 5682 

6-07 

394318 

2 

59 

5 7 3263 

5-21 

96721 -» 

• 85 

606046 

6-06 

393964 

1 

1 

5 7 35 7 5 

§•21 

967166 

• 85 

606410 

6* 06 

393590 

0 

c. 

Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang?- 

ML. 


(68 1) EG REES, ^ 





































40 


(22 DECREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

H 

0 

9*573575 

5*21 

9*967166 

.85 

9-606410 

6«o6 

io*3 9 35 9 o 

60 

i 

573888 

5*20 

967115 

*85 

606773 

6-06 

3 9 3227 

5 9 

2 

574200 

5*20 

967064 

*85 

607137 

6-o5 

392863 

58 

3 

574512 

5*19 

967013 

• 85 

607500 

6-o5 

3 9 25 jo 

57 

4 

574824 

5*19 

966961 

• 85 

607863 

6-04 

3 9 2 i 37 

56 

5 

576136 

5* 19 

966910 

• 85 

608225 

6-04 

391775 

55 

6 

575447 

5* 18 

966869 

• 85 

6o8588 

6-04 

391412 

54 

7 

5 j 5 j 58 

5* 18 

966808 

• 85 

608950 

6>o3 

3 9 io5o 

53 

8 

576069 

5 *i 7 

966756 

• 86 

609812 

6-o3 

390688 

52 

9 

576379 

5* 17 

966706 

• 86 

609674 

6 o3 

3 9 o 326 

5i 

10 

1 576689 

5 -16 

966653 

• 86 

6ioo36 

6-02 

389964 

5o 

ii 

9'576999 

5* 16 

9-966602 

• 86 

9-610397 

6-02 

10 38 9 6o3 

49 

12 

577309 

5-16 

96655o 

•86 

610709 

6-02 

389241 

48 

i3 

577618 

5 • 15 

966499 

• 86 

611120 

6-oi 

38888o 

47 

U 

577927 

5 • 15 

966447 

• 86 

611480 

6-oi 

388520 

46 

i5 

578236 

5 *i 4 

966396 

• 86 

611841 

6-oi 

38815 9 

45 

16 

578645 

5 *i 4 

966344 

• 86 

612201 

6-oo 

387799 

44 

I? 

578853 

5* i3 

966292 

• 86 

612561 

6-oo 

387439 

43 

18 

579162 

5* i3 

966240 

• 86 

612921 

6-oo 

387079 

42 

*9 

579470 

5* i3 

966188 

• 86 

613281 

5-99 

386719 

4i 

20 

5 79777 

5*12 

966136 

• 86 

61364i 

5.99 

38635 9 

4o 

21 

9*58oo85 

5*12 

9•966086 

.87 

9-614000 

5.98 

10-386000 

3q 

22 

58 o 392 

5 *ii 

966033 

.87 

6i435 9 

5.98 

385641 

38 

23 

680699 

5.11 

966981 

.87 

614718 

5.98 

385282 

37 

24 

58ioo5 

5.11 

966928 

•87 

615077 

5-97 

384923 

36 

25 

581312 

5* 10 

966876 

.87 

615435 

5-97 

384065 

35 

26 

581618 

5* 10 

965824 

.87 

615793 

5-97 

384207 

34 

27 

581924 

5.09 

965772 

•87 

6161 d 1 

5-96 

383849 

33 

28 

582229 

5*09 

966720 

•87 

6 i 65 o 9 

5*96 

383491 

32 

29 

582535 

5.09 

965668 

.87 

616867 

5*96 

383133 

3i 

3o 

582840 

5*08 

9656 i 5 

.87 

617224 

5.95 

3S2776 

3o 

3i 

9 * 583145 

5*o8 

9-965563 

.87 

9-617582 

5.95 

10-382418 

29 

32 

583449 

5*07 

9655 i1 

.87 

617939 

5- 9 5 

382061 

28 

33 

583754 

5*07 

9 65458 

.87 

618290 

5-94 

38 ito 5 

27 

34 

584 o 58 

5*06 

965406 

.87 

618662 

5-94 

381348 

26 

35 

58436 i 

5* 06 

965353 

• 88 

619008 

5-94 

380992 

25 

36 

584665 

5-06 

9653 oi 

• 88 

619364 

5-g3 

38o636 

24 

37 

584968 

5*o5 

966248 

• 88 

619721 

5.93 

380279 

23 

38 

585272 

5*o5 

965196 

• 88 

620076 

5.93 

379924 

22 

3 9 

585574 

5*04 

965143 

• 88 

620432 

5-92 

379.068 

21 

4o 

585877 

5* 04 

965090 

• 88 

620787 

5 • g2 

379213 

20 

4i 

9-586179 

5*o3 

9-965037 

• 88 

9-621142 

5- 9 2 

10*378858 

I 9 

42 

586482 

5*o3 

964984 

• 88 

621497 

5 - 91 

3785o3 

10 

43 

586 7 83 

5-o3 

964931 

• 88 

621852 

5-91 

378148 

17 

44 

587085 

5*02 

964879 

• 88 

622207 

5-go 

377793 

16 

45 

587386 

5*02 

964826 

• 88 

622661 

5-go 

377439 

i5 

46 

58 7 688 

5*oi 

964773 

• 88 

622915 

5-go 

377085 

i4 

47 

587989 

5*oi 

964719 

• 88 

623269 

5-89 

376731 

i3 

48 

588289 

5*oi 

964666 

.89 

623623 

5-89 

376.877 

12 

i 9 

588590 

5*oo 

964613 

.89 

628976 

5.89 

376024 

11 

5o 

688890 

5*oo 

964660 

• S 9 

624*30 

5-88 

375670 

10 

5i 

9*589190 

4*99 

9-964507 

• 8 9 

9-624683 

5-88 

10*375317 

O 

52 

589489 

4-99 

964454 

.89 

625o36 

5-88 

874964 

§ 

53 

589789 

4*99 

964400 

•89 

625388 

5-87 

374612 

7 

54 

590088 

4-9^ 

964847 

-89 

626741 

5-87 

374269 

6 

55 

590387 

4-98 

064294 

•89 

626093 

5-87 

373907 

5 

56 

590086 

4-97 

964240 

•89 

626445 

5-86 

373555 

4 

57 

590984 

4-97 

964187 

.89 

626797 

5-86 

373203 

3 

58 

591282 

4-97 

964133 

• 89 

627149 

5-86 

372851 

2 

5 9 

591680 

4-96 

964080 

.89 

627501 

5-85 

372499 

1 

60 

591878 

4-96 

964026 

• 89 

627852 

5-85 

372148 

0 

[_ 

Cosh e 

D. 

Sine 

D. 

Cotang. 
- 2_ 

D. 

Tang. 



(67 DEGREES.) 













































SINES AND TANGENTS. (23 DEGREES.) 


41 


M. 

Sine 

D. | 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

q. 591878 

4.96 

9.964026 

.89 

9-627862 

5-85 

10*372148 

60 

i 

592176 

4.95 

963972 

• 89 

628203 

5-85 

371797 

5o 

2 

692473 

4- 9 5 

963919 

.89 

628554 

5-85 

371446 

58 

3 

592770 

4-9° 

9 63865 

.90 

628905 

5-84 

371095 

5 ] 

4 

593067 

4.94 

9 638 i1 

.90 

629255 

5-84 

370745 

D6 

5 

5 q 3363 

4.94 

963757 

.90 

629606 

5-83 

370394 

55 

6 

593669 

4- 9 3 

963704 

.90 

62 99 56 

5-83 

370044 

54 

7 

598953 

4- 9 3 

9636D0 

.90 

63o3o6 

5-83 

369694 

53 

8 

594251 

4- 9 3 

9 635 9 6 

.90 

63o656 

5-83 

36 9 344 

52 

9 

594547 

4-92 

9 63D42 

.90 

63ioo5 

§•82 

368995 

5i 

IO 

5^4842 

4.92 

963488 

.90 

631355 

5*82 

368645 

5o 

ii 

9-595 i 37 

4 - 9 i 

9-963434 

.90 

9-631704 

5-82 

10-368296 

49 

12 

595432 

4 - 9 i 

963379 

.90 

632053 

5*8i 

367947 

48 

i3 

595727 

4 - 9 i 

96332 5 

.90 

632401 

5*8i 

367099 

47 

14 

596021 

4- 9 o 

963271 

.90 

632760 

5 • 81 

3672D0 

46 

ID 

5963 i 5 

4-90 

963217 

.90 

633o 9 8 

5* 80 

366902 

4D 

16 

596609 

4-89 

963i63 

.90 

633447 

5-80 

366553 

44 

l l 

5 9 6 9 o3 

4-89 

9 63108 

.91 

6337 9 5 

5* 80 

3662o5 

43 

i8 

597196 

4-89 

963oD4 

.91 

634143 

5-79 

365857 

42 

l 9 

59749° 

4-88 

962999 

.91 

634490 

5*79 

3655io 

4i 

20 

597783 

4-88 

962945 

.91 

634838 

5-79 

365 i 62 

40 

21 

9*598075 

4-87 

9-962890 

.91 

9 •635185 

5-78 

10•364815 

39 

22 

5 9 3368 

4-87 

962836 

.91 

635532 

5-78 

364468 

38 

23 

598660 

4-87 

962781 

.91 

635879 

5-78 

364121 

37 

24 

5 9 8 9 52 

4-86 

962727 

.91 

636226 

5-77 

363774 

36 

2D 

699244 

4-86 

962672 

•9i 

636572 

5-77 

363428 

35 

26 

599536 

4-85 

962617 

.91 

636 9 ! 9 

5-77 

363o8i 

34 

27 

§99827 

4-85 

962D62 

•9i 

637265 

5-77 

362735 

33 

28 

600118 

4-85 

9 625 o 8 

•91 

637611 

5*76 

362389 

32 

29 

600409 

4-84 

962453 

.91 

637966 

5-76 

362044 

31 

3o 

600700 

4-84 

962398 

.92 

638302 

5-76 

361698 

3o 

3i 

9-600990 

4.84 

9-962343 

-92 

9*638647 

5-75 

10-36i353 

29 

32 

601280 

4-83 

962288 

.92 

638 99 2 

5*75 

361008 

28 

33 

601070 

4-83 

962233 

•92 

63 9 337 

5-75 

36o663 

27 

34 

601860 

4-82 

962178 

.92 

639682 

5-74 

36o3i8 

26 

35 

602 I DO 

4-82 

962 I 23 

.92 

640027 

5-74 

359973 

25 

36 

602439 

4-82 

962067 

.92 

640371 

5*74 

359629 

24 

37 

602728 

4-8 i 

962012 

.92 

640716 

5-73 

359284 

23 

33 

603017 

4-8i 

961967 

.92 

641060 

5-73 

358940 

22 

3 9 

6o33o5 

4-8i 

961902 

.92 

6414o4 

5-73 

3585 9 6 

21 

4o 

603394 

4-8o 

961846 

.92 

641747 

5*72 

358253 

20 

4 i 

9 -6o3882 

4-80 

9-961791 

• 92 

9*642091 

5-72 

10-357909 


42 

604170 

4-79 

961735 

.92 

642434 

5-72 

357§66 

18 

43 

604457 

4-79 

961680 

.92 

642777 

5-72 

357223 

'I 

44 

6o4745 

4-79 

961624 

•93 

643120 

5-71 

35688o 

16 

45 

6 o 5 o 32 

4-78 

961569 

- 9 3 

643463 

5-71 

3560'* 

. iD 

46 

6o53i9 

4-78 

961513 

• 9 3 

6438o6 

5-71 

356 94 

14 

47 

6o56o6 

4-78 

961468 

• 9 3 

644148 

5-70 

3558 d 2 

i3 

48 

6o58 9 2 

4-77 

961402 

• 9 3 

644490 

5-70 

3555 io 

12 

49 

606179 

4-77 

961346 

• 9 3 

644832 

5.70 

355 68 

11 

5 0 

60646D 

4-76 

961290 

•93 

645174 

5-69 

354826 

10 

5 i 

9-606751 

4-76 

c* 9 6i235 

•9 3 

9.6455 i 6 

5.69 

10-354484 

2 

D2 

607036 

4-7 6 

9 6ii 79 

•9 3 

645357 

5-69 

354143 

8 

53 

607322 

4-7 5 

9 6 i1 23 

.9 

646199 

5-69 

3538oi 

7 

54 

607607 

4-70 

961067 

- 9 3 

646540 

§•63 

35346o 

6 


607892 

4-7-4 

961011 

• 9 3 

646881 

5*68 

353119 

5 

; 56 

608177 

4-74 

9 6o 9 55 

• 9 3 

647222 

5-68 

3D2778 

4 

St 

608461 

4-74 

960899 

• 9 3 

647562 

5-67 

352438 

3 

{ 58 

60874D 

4-78 

960843 

•94 

647903 

§•67 

352097 

2 

! 5 9 

609029 

4-73 

960786 

•94 

648243 

5*67 

351767 

1 

60 

6 o 9 313 

4-73 

960730 

•94 

648583 

5-66 

35i4i7 

0 


Cosine 

1 D. 

| Sine 

1 r. 

1 Cotang. 

I D. 

j Tang. 

M. 


(66 DEGREES.) 
























































42 


(24 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9*6c>93i3 

4-73 

9-960730 

•94 

9-648583 

5-66 

io-35i4i7 

60 

'I 

609597 

4-72 

960674 

(■94 

648923 

5-66 

351077 

5 9 

2 

609880 

4-72 

960618 

..•94 

649263 

5-66 

3007)7 

58 

3 

6ioj64 

4-72 

960561 

.94 

649602 

5-66 

350)98 

j?7 

4 

610447 

4-71 

96o5o5 

•94 

649942 

5-65 

35ooo8 

56 

5 

610729 

4-71 

960448 

.94 

660281 

5-65 

349719 

55 

6 

611012 

4-70 

960392 

.94 

65o62o 

5-65 

349)80 

54 

7 

611294 

4-70 

96o335 

•94 

650969 

5 • 64 

34041 

53 

8 

61iD76 

4-70 

960279 

-94 

651297 

5 • 64 

348703 

52 

9 

611858 

4-69 

960222 

r94 

651636 

5-64 

348)04 

5i 

lo 

612140 

4-69 

960166 

•94 

651974 

5-63 

348026 

5o 

1 

11 

9-612421 

4-69 

9-960109 

.95 

9-652312 

5-63 

10-347688 

49 

12 

612702 

4-68 

960002 

*90 

65265o 

5-63 

34735o 

48 

i3 

612983 

4-68 

909995 

.90 

65208 

5-63 

347012 

47 

14 

6i3264 

4-67 

959938 

190 

653326 

5-62 

34074 

46 

i5 

613545 

4-67 

959882 

-95 

653663 

5-62 

346337 

45 

16 

6i3820 

4-67 

959825 

- 9 5 

654ooo 

5-62 

346000 

44 

• 7 

6i4io5 

4-66 

959768 

• 90 

654337 

5-6i 

345663 

43 

i8 

614385 

4-66 

909711 

.95 

654674 

5-6i 

345326 

42 

>9 

614665 

4-66 

969654 

- 9 5 

655oi1 

5-6i 

34409 

41 ! 

20 

614944 

4-65 

959096 

• 90 

655348 

5-6i 

344602 

4o 

21 

9-6i5223 

4-65 

q-o5q53q 

•9 5 

9-655684 

5-6o 

io-3443i6 

39 

22 

6i55o2 

4-65 

969482 

.90 

656o2o 

5-6o 

34300 

38 

23 

615781 

4-64 

959425 

.90 

656356 

5-6o 

343644 

3? 

24 

616060 

4-64 

959)68 

.90 

656692 

5-59 

3433o8 

36 

25 

616338 

4-64 

959310 

• 96 

657028 

5-59 

342972 

35 

26 

616616 

4-63 

959253 

• 96 

657364 

5.59 

3426)6 

34 

27 

616894 

4-63 

959195 

• 96 

657699 


3423oi 

33 

28 

6i7n2 

4-62 

959138 

• 96 

658o34 

5-58 

34106 

32 

29 

617460 

4-62 

959081 

•96 

65836q 

5-58 

341631 

3i 

3o 

617727 

4-62 

969023 

•96 

658704 

5-58 

341296 

3o 

31 

9-618004 

4-6i 

9-968965 

•96 

9-659039 

5-58 

10-340961 

2 9 

32 

618281 

4-6i 

958908 

.96 

65073 

5*57 

340627 

28 

33 

618558 

4-6i 

958o5o 

•0 

659708 

5-57 

340292 

27 

34 

6i8834 

4-60 

958792 

•0 

660042 

5-57 

3399)8 

26 

35 

619110 

4 - 60 

968734 

•0 

660376 

5-57 

339624 

25 

36 

619386 

4-6o 

958677 

•0 

660710 

5-56 

339290 

24 

37 

619662 

4-09 

958619 

•0 

66io43 

5-56 

338957 

2) 

38 

619938 

4-69 

958561 

•0 

661377 

5-56 

338623 

22 

3 9 

620213 

4-5 9 

9585o3 

•97 

661710 

5-55 

338290 

21 

40 

620488 

4* 5o 

958445 

•97 

662043 

5-55 

3379)7 

20 

41 

9-620763 

4* 58 

9-958387 

•97 

9-662376 

5-55 

10-337624 

IO 

42 

621038 

4*57 

958329 

•97 

662709 

5-54 

337291 

i8 

43 

621313 

4*57 

958271 

•97 

03o42 

5-54 

336958 

17 

44 

621087 

4-07 

9582i3 

•97 

663375 

5-54 

33605 

16 

40 

621861 

4-56 

958i54 

•97 

663707 

5-54 

336298 

i5 

46 

622135 

4-56 

958096 

•97 

664089 

5-53 

33501 

14 

4 7> 

622409 

4-56 

9580)8 

•97 

664371 

5-53 

335629 

i3 

48 

622682 

4-55 

957979 

•97 

664703 

5-53 

335297 

12 

49 

622906 

4-55 

967921 

•97 

665o35 

5-53 

33405 

11 

5o 

623229 

4-55 

907863 

•97 

665366 

5-52 

334634 

10 

5i 

9-6235o2 

4-54 

9-957804 

♦97 

9-665697 

5-52 

io-3343o3 

9 

- 52 

623774 

4-54 

957746 

•0 

666029 

5-52 

333971 

8 

53 

624047 

4-54 

967687 

•0 

66636o 

5-5i 

33364c 

7 

54 

624319 

4-53 

967628 

♦98 

666691 

5 • 51 

333309 

6 

55 

624091 

4-53 

957670 

•98 

667021 

5-5i 

332979 

5 

56 

624863 

4-53 

967511 

•98 

667352 

5 - 51 

332648 

j 4 

5 I 

620i35 

4-52 

957452 

-0 

667682 

5-5o 

3323i8 

3 

58 

620406 

4-52 

967393 

•0 

668013 

5-5o 

331987 

2 

59 

626677 

4-52 

907335 

•0 

668343 

5-5o 

33107 

1 

60 

626948 

4«5 i 

967276 

•98 

668672 

5-5o 

33i328 

0 

: ~7; 

Cosine 

D. 

Sine 

D. 

Cotang. 

Lj^ 

Tang. 

M. 


(05 DEGREES.) 






























































SINES AND TANGENTS. (25 DEGREES.) 43 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

• 

o 

9-625948 

4 - 5 1 

9.957276 

• 98 

9-668673 

5 - 5 o 

io* 33 i 327 

60 

i 

626219 

4 - 5 i 

967217 

• 98 

669002 ' 

5*49 

330098 

5 9 

2 

626490 

4 - 5 i 

957158 

• 98 

669332 

5*49 

33 o 6 o 8 

58 

3 

626760 

4 - 5 o 

957099 

• 98 

669661 

5-49 

33 o 339 

57 

4 

627030 

4 - 5 o 

957040 

• 98 

669991 

5.48 

330009 

56 

5 

627300 

4 - 5 o 

956981 

.98 

670)20 

5-48 

329680 

55 

6 

627670 

4.49 

956921 

*99 

670649 

5-48 

329351 

54 

7 

627840 

4.49 

956862 

•99 

670977 

5-48 

329023 

53 

8 

628109 

4.49 

906803 

•99 

671)06 

5-47 

328694 

52 

9 

628378 

4.48 

966744 

•99 

671634 

5-47 

328366 

5 i 

10 

628647 

4-48 

956684 

•99 

67:963 

5-47 

328037 

5 o 

ii 

9*628916 

4-47 

Q -956625 

•99 

)-67229i 

5-47 

10-327709 

49 

12 

629185 

4*47 

956066 

•99 

672619 

5-46 

327)81 

48 

i 3 

629453 

4*47 

956506 

•99 

672947 

5*46 

327053 

47 

14 

629721 

4.46 

956447 

•99 

673274 

5-46 

326726 

46 

i 5 

629989 

4-46 

966387 

•99 

673602 

5-46 

326)98 

45 

16 

630267 

4-46 

956327 

•99 

673929 

5-45 

326071 

44 

17 

63o524 

4.46 

956268 

•99 

674257 

5-45 

325743 

43 

18 

630792 

4-45 

966208 

I -00 

674584 

5-45 

325416 

42 

19 

631069 

4-45 

966148 

I -00 

674910 

5-44 

325090 

4 i 

20 

631 3 26 

4-43 

956089 

I -00 

676237 

5-44 

324763 

4 o 

21 

9- 63 1593 

4-44 

9-956029 

I -00 

9-675564 

5*44 

io *324436 

39 

22 

63 i 85 o 

4*44 

955969 

I -00 

675890 

5*44 

324110 

38 

23 

632123 

4.44 

955909 

I -00 

676216 

5*43 

323784 

37 

24 

632392 

4-43 


I -00 

676543 

5-43 

323457 

36 

25 

632658 

4-43 

955789 

I -oo 

676869 

5*43 

323 1 3 1 

35 

26 

632923 

4*43 

955729 

I -00 

677194 

5*43 

322806 

34 

27 

633 i 8 g 

4*42 

955669 

1 -00 

677520 

5*42 

322480 

33 

28 

633464 

4-42 

955609 

I -00 

677846 

5*42 

322 i 54 

32 

29 

633719 

4-42 

955548 

I -00 

678171 

5-42 

321829 

3 i 

3 o 

633984 

4-41 

955488 

I -00 

678496 

5-42 

32 i 5 o 4 

3 o 

3 i 

9-634249 

4 - 4 i 

9-955428 

I -01 

9*678821 

5-41 

10*321179 

29 

32 

6345 i 4 

4*40 

955368 

I -01 

679146 

5 • 4 1 

320854 

28 

33 

634778 

4 * 4 o 

955307 

I -01 

679471 

5 - 4 i 

320529 

27 

34 

635o42 

4.40 

955247 

1 -01 

679795 

5 - 4 i 

320205 

26 

35 

6353 o 6 

4-39 

955 i 86 

I -01 

6S0120 

5 - 4 o 

3 19880 

25 

36 

635570 

4-39 

955 i 26 

I -01 

680444 

5 - 4 o 

3 i 9556 

24 

37 

635834 

4-39 

955 o 65 

I -01 

680768 

5 - 4 o 

319232 

23 

38 

636097 

4-38 

955 oo 5 

I -01 

681092 

5 * 4 o 

3 18908 

22 

39 

63636 o 

4 - 38 

954944 

1 -01 

681416 

5.39 

3 1 8584 

21 

40 

636623 

4*38 

9 54883 

I -01 

681740 

5.39 

3i?26o 

20 

41 

9*636886 

4*37 

9-954823 

I -01 

9-682063 

5-39 

10-317937 

10 

42 

637148 

4-37 

954762 

I -01 

682387 

5 - 3 9 

31761) 

10 

43 

637411 

4*37 

954701 

I -01 

682710 

5-38 

317290 

17 

44 

637673 

4-37 

964640 

I -01 

683 o 33 

5-38 

3 16967 

l6 

45 

637935 

4 * 36 

954579 

I -01 

683356 

5-38 

3 i 6644 

i 5 

46 

638197 

4-36 

954518 

I -02 

683679 

5-38 

3 1 632 1 

14 

47 

638458 

4-36 

954457 

I -02 

684001 

5-37 

3 15999 

i 3 

48 

638720 

4-35 

954396 

I -02 

684324 

5-37 

3 15676 

12 

49 

638981 

4-35 

954335 

I -02 

684646 

5-37 

3 1 5354 

11 

5 o 

639242 

4*35 

964274 

1*02 

684968 

5-37 

3 i 5 o 32 

10 

5 i 

9 * 6395 o 3 

4-34 

9-95421 3 

1-02 

9-685290 

5-36 

10- 3 i4710 

2 

52 

639764 

4-34 

954 i 52 

I -02 

6856 n 

5-36 

314)88 

0 

53 

640024 

4*34 

954090 

1-02 

685984 

5*36 

3 14066 

7 

54 

640284 

4-33 

954029 

I -02 

686255 

5-36 

3 i 3745 

6 

55 

640544 

4-33 

953968 

I -02 

686577 

5-35 

3 1 3423 

5 

56 

640804 

4-33 

953906 

I -02 

686898 

5*35 

3 1 3 102 

4 

5 i 

641064 

4-32 

953845 

1-02 

687219 

5-35 

312781 

3 

58 

641324 

4-32 

953783 

1 -02 

687540 

5*35 

3 12460 

2 

5 9 

64 i 584 

4-32 

953722 

1 -o 3 

687861 

5-34 

3 12139 

1 

60 

641842 

4 • 3 1 

953660 

I -o 3 

688182 

5-34 

3 i 1818 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tan<r. 

M. 

— — - 


(G4 DEGREES.) 
























































44 


(26 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine ' D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

1 

| 

: o 

i 

a 

3 

4 

5 

6 

7 

6 

9 

IC 

11 

12 

1 3 

14 

1 5 

16 

17 

18 

19 

20 

21 
33 

23 

24 
20 
26 

27 

28 

12 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

40 

4 1 

42 

43 

44 

45 

46 

47 

48 

49 

5 0 

5 1 

52 

53 

54 

55 

56 

57 

58 

5 9 

60 

9-641842 
642101 
642860 
642618 
642877 
6431 35 
643393 
643600 
643908 
644160 
644423 

9•644680 
644936 
6451 Q 3 

645400 

640706 

645962 

646218 

646474 

646729 

646984 

9-647240 

647494 

647749 

648004 

648258 

648012 

648766 

649020 

649274 

649627 

9-649781 
65 oo 34 
650287 
65 oo 39 
660792 
65 1044 
601297 
65 1049 
65 1800 
652002 

9 - 6523 o 4 

652555 

602806 

653 o 57 

6533 o 8 

653558 

6538 o 8 

654059 

654309 

654558 

9-664808 

655 o 58 

655307 

655556 

6558 o 5 

656 o 54 

6563 02 
65655 1 
606799 

657047 

4 - 3 i 

4 - 3 i 

4 - 3 i 

4 - 3 o 

4 - 3 o 

4 - 3 o 

4 - 3 o 

4-29 

4-29 

4-29 

4-28 

4-28 

4-28 

4-27 

4-27 

4-27 

4-26 

4-26 

4-26 

4-25 

4-25 

4-25 

4-24 

4-24 

4-24 

4-24 

4-23 

4-23 

4-23 

4-22 

4-22 

4-22 

4-22 

4-21 

4-21 

4-21 

4-20 

4-20 

4-20 

4 -19 

4 -19 

t\t 

4 -18 

4-18 

4-18 

4-17 

4-17 

4-17 

4 -16 

4-16 

4 -16 

4-16 

4 -1 5 

4-15 

4-15 
4-14 

4-14 

4-14 

4-13 

4-13 

9-963660 

953599 

953537 

953475 

9534 i 3 

953352 

963290 

953228 

953166 

953 io 4 

953042 

9-952980 

902918 

952855 

902793 

952731 

902669 

952606 

952544 

952481 

952419 

9-952356 

952294 
952231 
952168 
952106 
952043 
951980 
951017 
95 i 854 
95 1 79 1 

9-951728 
951 665 
951602 
95 [539 
951476 
951412 
901349 
951286 
951222 
951159 

9-951096 

951082 

900968 

950905 

950841 

960778 

960714 

95 o 65 o 

950086 

95 o 522 

9-960458 
960394 
95o33o 
960266 
950202 
9601 38 
960074 
950010 

949945 

949881 

1 -o 3 

1 -o 3 

1 -o 3 

1 -o 3 

1 -o 3 

1 -o 3 

1 -o 3 

1 -o 3 

1 -o 3 

1 -o 3 

1 -o 3 

1 • 04 

1 • 04 

1 -04 

1 • 04 

1 • 04 

1 -04 

1 -04 

1 • 04 

1 -04 

•*•04 

1 • 04 

1 -04 

1 -04 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -o 5 

1 -06 

1 -06 

1 -06 

1 -06 

1 -06 

1 -06 

1 -06 

1 -06 

1 -06 

1 -06 

1 -06 

1 -06 

1 -06 
1-07 

1-07 

1-07 

1-07 

1.07 

1-07 
1-07 

1 -07 

1 " 07 

1-07 

1 -07 

9-688182 

6885 o 2 

688823 

689143 
689463 
689783 
6901o 3 
690423 
690742 
691062 
691381 

9-691700 

692019 

692338 

692666 

692975 

693293 

693612 

693930 

694248 

694666 

9-694883 

696201 

695518 

695836 

696153 

696470 

696787 

697108 

697420 

697736 

9-698053 
698369 
698686 
699001 
699316 
699632 
699947 
700263 
700578 
700893 

9-701208 

7 oi 523 

701837 

702152 

702466 

702780 

703095 

703409 

703728 

704036 

9-7o435o 

704663 

704977 

705290 

7 o 56 o 3 

705916 

706228 

706541 

706854 

707166 

5.34 

5-34 

5-34 

5-33 

5-33 

5-33 

5-33 

5-33 

5-32 

5-32 

5-32 

5 - 3 1 

5 • 31 

5 - 3 1 

5 * 3 1 

5 • 3 1 
5 - 3 o 
5 - 3 o 
5 - 3 o 

5 - 3 o 

6- 29 

6-29 

5- 29 

6- 29 
5-29 
5-28 
5-28 
5-28 
5-28 
5-27 
5*27 

5-27 

5-27 

5-26 

5-26 

5-26 

5-26 

5-26 

5-25 

5-25 

5-25 

5-24 

5-24 

5-24 

5-24 

5-24 

5-23 

5-23 

5-23 

5-23 

5-22 

5-22 

5-22 

5-22 

5-22 

5-21 

5-21 

5-21 

5-21 

5-21 

5-20 

io- 3 i1818 

3 11498 
311177 

3 10867 
3 io 537 
310217 
309897 
309577 
309268 
^08938 
308619 

is- 3 o 83 oo 

307981 

307662 

307344 

307028 

306707 

3 o 6388 

306070 

305782 

3 o 5434 

io- 3 o 5 i17 
304799 
304482 
304164 
3 o 3847 
3 o 353 o 
3 o 32 i 3 
3 o 2 S(^*| 
3 o 258 o 
302264 

10.301947 
3 o1 63 1 
3 o1 3 1 5 
300999 
300684 
3 oo 368 
3 ooo 53 
299737 
299422 
299107 

10-298792 

298477 

298163 

297848 

297534 

297220 

296900 

296091 

296277 

295964 

10* 295650 
295337 
29O023 
294710 
294307 
294084 
298772 
298459 
298146 
292834 

60 

58 

3 

55 

54 

53 

5 a 

5 i 

5 o 

§ 

47 

46 

45 

44 

43 

42 

4 i 

4 o 

3 9 

38 

37 

36 

35 

34 

33 1 
32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

I9 

l8 

J 7 

16 

i 5 

14 

i 3 

12 

11 

10 

7 

6 

5 

4 

3 

2 

1 

0 

■ 

Cosine D. 

Sine 

I). 

Cotang. 

D. 

Tang. 

M. 


(63 DEGREE8.) 






















































SINES AND TANGENTS. (27 DEGREES.) 45 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-667047 

4-i3 

9-949881 

1-07 

9-707166 

5-20 

10-292834 

60 

i 

657296 

4* i3 

949816 

1 -07 

707478 

5-20 

292522 

DO 

i 

657542 

4-12 

949702 

1 -07 

707790 

5-20 

292210 

58 

3 

4 

60779c 

658o37 

4’ 12 

4’ 12 

949688 

949623 

1 -08 

1 -08 

708102 

708414 

5-20 

5-19 

291898 

291686 

57 

56 

5 

668284 

4* 12 

949558 

1 -08 

708726 

5-19 

291274 

5o 

6 

658531 

4 • 11 

949494 

1 -08 

709037 

5-19 

290963 

54 

7 

658778 

4* 11 

949429 

i-08 

709349 

5-19 

290651 

53 

8 

609025 

4-11 

949364 

1 -08 

709660 

5-19 

290340 

52 

9 

659271 

4-10 

949300 

1 -08 

70997 1 

5-18 

290029 

5i 

10 

659517 

4-10 

949235 

1 -08 

710282 

5-i8 

289718 

5o 

ii 

9-659763 

4 - 10 

9-94917° 

1 -o3 

9-710593 

5-18 

10-289407 

49 

12 

660009 

4-09 

949105 

1 -08 

710904 

5-18 

289096 

48 

i3 

660200 

4-09 

949040 

948975 

1 -08 

711215 

5-18 

288785 

47 

14 

66o5oi 

4'09 

1 -08 

711625 

5-17 

288475 

46 

i5 

660746 

4*09 

948910 

948845 

1 -08 

711836 

5-17 

288164 

45 

16 

660991 

4-08 

1 -08 

712146 

5-17 

287864 

44 

17 

661286 

4*o8 

948780 

1 -09 

712466 

5-17 

287644 

43 

18 

661481 

4-o8 

948715 

1 -09 

712766 

5-i6 

287234 

42 

19 

661726 

4-07 

94865o 

1 -09 

713076 

5-i6 

286924 

4i 

20 

661970 

4-07 

948684 

1 -09 

7i3386 

5 -16 

286614 

40 

21 

9-662214 

4-07 

9-q485i9 

1-09 

9-713696 

5-16 

io- 2863 o 4 

3 9 

22 

662459 

4-07 

948454 

1-09 

714006 

5-16 

286996 

38 

23 

662703 

4-06 

948388 

1 -09 

714314 

5 • 15 

285686 

37 

24 

662946 

4*o6 

948323 

1 -09 

714624 

5 • 15 

285376 

36 

25 

663190 

4-06 

948267 

1 -09 

714933 

5 • 15 

286067 

35 

26 

663433 

4*o5 

948192 

1-09 

716242 

5 -15 

284768 

34 

27 

663677 

4-o5 

948126 

1 -09 

7 1 555i 

5-14 

284449 

33 

28 

663920 

4 - o5 

948060 

1 -09 

71586o 

5-14 

284140 

32 

29 

664163 

4*o5 

947995 

1 • 10 

716168 

5-i4 

283832 

3i 

3o 

664406 

4 ‘o 4 

947929 

1 • 10 

716477 

5-14 

283523 

3o 

3i 

9-664648 

4 -o 4 

9-947863 

1 • 10 

9-716785 

5 • 14 

io-2832i5 

29 

32 

664891 

4 -o 4 

947797 

947701 

1 • 10 

7 1 7 0 93 

5-13 

282907 

28 

33 

665 1 33 

4’o3 

1 • 10 

717401 

5 - 13 

282699 

27 

34 

665375 

4*o3 

047665 

1 • 10 

717709 

5 • 13 

282291 

26 

35 

665617 

4-o3 

947600 

1 • 10 

718017 

5 • 13 

281983 

25 

36 

666869 

4’02 

947533 

1 • 10 

718326 

5 • 13 

281670 

24 

37 

666100 

4'02 

947467 

I -10 

7 i 8633 

5-12 

281367 

23 

38 

666342 

4‘02 

947401 

1 • 10 

718940 

5-12 

281060 

22 

39 

666583 

4‘02 

947335 

1 • 10 

719248 

5-12 

280762 

21 

4o 

666824 

4 ’oi 

947269 

1 • 10 

719555 

5-12 

28o445 

20 

4i 

9-667065 

4-oi 

9-947203 

1 • 10 

9.719862 

5-12 

io- 28 oi 38 

*9 

42 

667305 

4-oi 

947136 

1 • 11 

720169 

5. II 

279831 

18 

43 

667546 

4'oi 

947070 

1 • 11 

720476 

5 • 11 

279624 

17 

44 

667786 

4'oo 

947004 

1 • 11 

720783 

5-11 

279217 

16 

45 

668027 

4-oo 

946937 

946871 

1 • 11 

721089 

5-n 

278911 

i5 

46 

668267 

4’oo 

1 • 11 

721396 

5-11 

278604 

, i4 

47 

6685o6 

3*99 

946804 

1 • 11 

721702 

5-io 

278298 

i3 

48 

668746 

8'99 

946738 

1 • 11 

722009 
722315 

5-io 

277991 

12 

49 

66S986 

3-99 

946671 

1 • 11 

5-io 

277680 

11 

5o 

669226 

3-99 

946604 

1 • 11 

722621 

5-io 

277379 

JO 

5i 

9 • 669464 

3- 9 8 

9-946538 

1 • 11 

9.722927 

5-io 

10-277073 

9 

52 

669703 

3-98 

946471 

1 • 11 

723232 

5-09 

276768 

8 

53 

669942 

3-98 

946404 

1 • 1 1 

723538 

5-oq 

276462 

7 

54 

670181 

3*97 

946337 

in 

723844 

5-09 

276156 

6 

55 

670419 

3-97 

946270 

1 • 12 

724149 

5-09 

275801 

5 

56 

670658 

3.97 

946203 

1-12 

724454 

5-09 

275546 

4 

57 

670896 

3-97 

946136 

I -12 

724769 

5-08 

276241 

3 

58 

671134 

3*96 

946069 

1-12 

725 o 65 

5-08 

274935 

2 

5g 

671372 

3-96 

946002 

I • 12 

725369 

5-08 

274631 

1 

60 

671609 

3-96 

945935 

I • 12 

726674 

5-08 

274326 

0 


Coaine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(62 DEGREES.) 








































46 


(28 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

o 

9-671609 

3-96 

9-945935 

1*12 

9-726674 

5 08 

10-274326 

i 

671847 

3-95 

945868 

I • 12 

725979 

5 08 

274021 

3 

672084 

3- 9 5 

945800 

1-12 

726284 

5-07 

273716 

3 

672321 

3- 9 5 

945733 

I • 12 

,26588 

5-07 

273412 

4 

672558 

3-95 

945666 

I • 12 

726892 

5-07 

273108 

5 

672795 

3-94 

945598 

945531 

I • 12 

727197 

5-07 

272803 

e 

673082 

3-94 

I • I 2 

727501 

5-07 

272499 

7 

673268 

3-94 

945464 

i • 13 

727805 

5-06 

272193 

8 

6735o5 

3-94 

945396 

1 • i3 

728109 

5-06 

271891 

271688 

c 

673741 

3- 9 3 

945328 

1 -13 

728412 

5-06 

10 

6739-’'’ 

3-93 

946261 

1 • i3 

728716 

5-06 

271284 

11 

9 674210 

3-9? 

9-946193 

1 -i3 

9-729020 

5-06 

10-270980 

12 

674448 

3-92 

946125 

1 • 13 

729323 

5-o5 

270677 

i3 

674684 

3-92 

945o58 

1 • 13 

729626 

5-o5 

270374 

14 

15 

674919 

675 i 55 

3-92 

3-92 

944990 

944Q22 

944854 

1 • i3 

1 • i3 

729929 

730233 

5-o5 

5-o5 

270071 

269767 

16 

675390 

3-91 

1 • i3 

73o535 

5-o5 

269465 

17 

676624 

3-91 

944786 

1 • i3 

73 o 838 

5-04 

269162 

268839 

18 

676859 

3-91 

944718 

1 • i3 

73 ii 4 i 

5-o4 

19 

676094 

3-91 

94465 o 

1 • 13 

731444 

5-o4 

268556 

20 

676328 

3-90 

944682 

1*14 

731746 

5-o4 

268264 

21 

9-676662 

3-90 

9-9445 i 4 

1 • 14 

9-732048 

5-04 

10-267952 

22 

676796 

3-90 

944446 

1-14 

73235 i 

5-o3 

267649 

23 

677030 

3-90 

9^4377 

1 * 14 

732653 

5-o3 

267347 

24 

677264 

3-89 

944309 

i-14 

732955 

5-o3 

267045 

25 

677498 

3-89 

944241 

i-14 

733257 

5-o3 

266743 

26 

677731 

3-89 

944172 

1 • i4 

733558 

5-o3 

266442 

s 7 

677964 

3-88 

944104 

1 • 14 

73386 o 

5-02 

266140 

28 

678197 

3-88 

944036 

1 -14 

734162 

5-02 

265838 

29 

678440 

3-88 

943967 

1 * 14 

734463 

5-02 

265537 

3o 

678663 

3-88 

943899 

1 • :4 

734764 

5-02 

265236 

3i 

9-678895 

3-87 

9-94383o 

i-i 4 

9*735 o 66 

5-02 

10-264934 

32 

679128 

3-87 

943761 

1 • 14 

735367 

5-02 

264633 

33 

679360 

3-8 7 

943693 

1 - 15 

735668 

5-oi 

264332 

34 

679592 

3-87 

943624 

1 • 15 

735969 

5-oi 

264031 

35 

679824 

3-86 

943555 

1 • 15 

736269 

5-oi 

263731 

36 

68oo56 

3-86 

943486 

1 • 15 

736570 

5-oi 

26343o 

37 

680288 

3-86 

943417 

1 - 15 

736871 

5-oi 

263129 

38 

680519 

3-85 

943348 

1 • 15 

737171 

5-oo 

262829 

39 

680750 

3-85 

943279 

1 • 15 

737471 

5-oo 

262629 

40 

680982 

3-85 

943210 

1 • 1 5 

737771 

5-oo 

262229 

4i 

9 - 681213 

3-85 

9-943141 

1 • 15 

9-738071 

5-oo 

10-261929 

42 

681443 

3-84 

943072 

1 • i5 

738371 

5-oo 

261629 

43 

681674 

3-84 

943 oo 3 

1 • 15 

738671 

4-99 

261329 

44 

681905 

3-84 

942934 

1 -15 

738971 

4-99 

261029 

45 

682135 

3-84 

942864 

1 • i5 

739271 

4-99 

260729 

46 

682365 

3-83 

94279 5 

1 • 16 

739570 

4-99 

260430 

47 

682696 

3-83 

942726 

1 -16 

739870 

4-99 

26 oi 3 o 

48 

682825 

3-83 

942666 

1 -i6 

740160 

4-99 

269831 

49 

683o55 

3-83 

942687 

1 • 16 

740468 

4-98 

269332 

5o 

688284 

3-82 

942517 

1 • 16 

740767 

4-98 

259233 

5i 

9*6835i4 

3-82 

9-942448 

1 * 16 

9-741066 

4-98 

10-258934 

52 

683743 

3-82 

942378 

1 • 16 

741365 

4-98 

258635 

53 

683972 

3-82 

9423 o 8 

1 • 16 

741664 

4-98 

258336 

54 

684201 

3 • 81 

942239 

1 • 16 

741962 

4-97 

258 o 38 

55 

684430 

3 • 81 

942169 

i-16 

742261 

4-97 

267739 

56 

684668 

3 • 8 1 

942099 

1 -16 

742559 

4-97 

257441 

57 

684887 

3-80 

942029 

1 • 16 

742858 

4-97 

267142 

58 

685115 

3-80 

941969 

1 • 16 

743156 

4-97 

256844 

59 

685343 

3-8o 

941889 

i-i 7 

743454 

4-97 

256546 

60 

685571 

3-80 

941819 

l ' 1 l 

743752 

4.96 

266248 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 



l 

7 

o 

5 

4 

3 

3 

1 

O 


M. 




J 


(61 DEGREES.) 


IOMMMIOMWIOMIO WWWOJWWWWOJW O' O'U>0> Ol Ol Ol 

O — »0 Wi^ U1 O'—I QOO O H W w;\ 01^ QOO O M lO UiJ>. Uiff'-J CCO o " M V> 0 '~J OOO o — UK WiO'-J 






























































SINES AND TANGENTS. (29 DEGREES.) 47 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9 685571 

3-8o 

9-941819 

1 * 17 

9-743752 

4.96 

lo -256248 

60 

i 

685799 

3-79 

941749 

1 * 17 

744 o 5 o 

4.96 

255960 


2 

686027 

3-79 

941679 

1 * 17 

744348 

4.96 

25 o 652 

58 

3 

686254 

3-79 

941609 

1*17 

744645 

4.96 

255355 

67 

4 

686482 

3-79 

941539 

1 * 17 

744943 

4.96 

255 o 57 

56 

5 

686709 

3-78 

941469 

i-i7 

745240 

4-96 

254760 

55 

6 

686g36 

3-78 

941398 

i -17 

745538 

4-90 

254462 

54 

7 

687163 

3 • 78 

941328 

1 -17 

745835 

4-96 

264166 

53 

8 

687389 

3-78 

941258 

1 • 17 

746132 

4-96 

253868 

62 

9 

687616 

3.77 

941187 

1*17 

746429 

4-96 

253571 

5i 

IO 

687843 

3.77 

941117 

i*i 7 

746726 

4-q5 

253274 

5o 

11 

9-688069 

3-77 

9-941046 

1 • 18 

9-747023 

4-94 

10 252977 

49 

12 

688290 

3-77 

940975 

1 • 18 

747319 

4.94 

25268 i 

48 

i3 

688521 

3.->6 

940905 

1 • 18 

747616 

4-94 

202384 

47 

14 

688747 

3-76 

940834 

1 • 18 

7479^ 

4-94 

252087 

46 

i5 

688972 

3.76 

940763 

1 • 18 

748209 

4.94 

251791 

45 

16 

689198 

3.76 

940693 

1 • 18 

7485 o 5 

4-93 

201495 

44 

n 

689428 

3-75 

940622 

1 • 18 

\ 748801 

4.93 

25ii99 

43 

18 

689648 

3.75 

94o551 

1*18 

749097 

4.93 

250908 

42 

19 

689873 

3. 7 5 

940480 

1 • 18 

7493o3 

4-93 

260607 

4i 

20 

690098 

3- 7 5 

940409 

1 • 18 

749689 

4.93 

25 o 3 ii 

40 

21 

9-690323 

3-74 

9-94o338 

1*18 

9-749985 

4-93 

io- 25 ooi 5 

3q 

22 

690548 

3.74 

940267 

1 • 18 

760281 

4-92 

249719 

38 

23 

690772 

3-74 

940196 

1*18 

760676 

4.92 

249424 

37 

24 

690996 

3-74 

940125 

1-19 

750872 

4-9 2 

249128 

36 

25 

691220 

3.73 

940054 

i-i 9 

761167 

4-92 

248833 

35 

26 

691444 

3.73 

939982 

1 • 19 

751462 

4.92 

248538 

34 

27 

691668 

3-73 

939911 

1 • 19 

751767 

4.92 

248243 

33 

28 

691892 

3- 7 3 

939840 

1 • 19 

7 52052 

4-91 

247948 

32 

29 

6921i5 

3*72 

989768 

1 • 19 

752347 

4-9 1 

247653 

3i 

3o 

692339 

3-72 

939697 

1-19 

752642 

4-91 

247358 

3o 

3i 

9-692562 

3*72 

9-939625 

1-19 

9-752937 

4.91 

10-247063 

29 

32 

692785 

3-71 

939554 

1-19 

75323 i 

4-91 

246769 

28 

33 

693008 

3-71 

989482 

1-19 

753526 

4.91 

246474 

27 

34 

693231 

3.71 

939410 

1-19 

753820 

4.90 

246180 

26 

35 

693453 

3.71 

939339 

1-19 

754 ii 5 

4.90 

245885 

20 

36 

693676 

3-70 

939267 

1 • 20 

754409 

4.90 

245591 

24. 

37 

693898 

3-70 

989196 

1 • 20 

754703 

4.90 

245297 

23 

38 

694120 

3-70 

939123 

1 • 20 

754997 

4.90 

245 oo 3 

22 

39 

694342 

3-70 

989062 

I -20 

755291 

4.90 

244709 

21 

40 

694564 

3-69 

938980 

1-20 

755585 

4.89 

244416 

20 

4i 

9-694786 

3-69 

9-988908 

1-20 

9-755878 

4.89 

10-244122 

IO 

42 

695007 

3-69 

938836 

1-20 

756172 

4.89 

243828 

l8 

43 

696229 

3-69 

988768 

1-20 

756465 

4.89 

243535 

17 

44 

695450 

3-68 

988691 

I -20 

756759 

4.89 

243241 

l6 

j 45 

696671 

3-68 

988619 

1-20 

757062 

4.89 

242948 

i5 

46 

690892 

3-68 

988547 

I -20 

757345 

4-88 

242655 

i4 

47 

6961i3 

3*68 

988476 

I -20 

757638 

4-88 

242862 

r3 

48 

690334 

3 ‘67 

938402 

I -21 

757981 

4-88 

242069 

12 

49 

696004 

3-6 7 

q3833o 

I -21 

758224 

4-88 

241776 

11 

j 5o 

696775 

3-67 

988208 

I - 21 

758617 

4.88 

241483 

10 

5i 

0-696995 

3-67 

9-938185 

I -21 

9-758810 

4.88 

10-241190 

9 

52 

697216 

3-66 

988113 

1 -21 

'] 5 g \02 

4.87 

240898 

8 

53 

697435 

3-66 

938040 

I - 21 

759395 

4.87 

24 o 6 o 5 

7 

54 

697654 

3-66 

937967 

I -21 

759687 

4.87 

24 o 3 i 3 

6 

55 

697874 

3 - 66 

987896 

I -21 

769979 

4-87 

240021 

5 

56 

698094 

3-65 

937822 

I • 21 

760272 

4-87 

239728 

4 

5 7 

6 9 8313 

3-65 

937749 

I -21 

760564 

4-87 

23q436 

3 

58 

698032 

3-65 

937676 

I - 21 

760866 

4-86 

289144 

2 

59 

698701 

3-65 

937604 

I • 21 

761148 

4-86 

238852 

I 

60 

698970 

3.64 

93 7 53i 

I • 21 

761439 

4-86 

23856j 

0 


Cosine 

D. 

Sine 

D. 

-' 

Cotang. 

D. 

Tang. 

M. 


27 (60 ^DEGREES.) 








































48 (30 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9>698970 
699109 

3-64 

9-937531 

1*21 

9-761439 

4-86 

io-238561 

60 

i 

3-64 

937458 

1-22 

761731 

4-86 

238269 

5 o 

2 

699407 

3-64 

937385 

1-22 

762023 

4-86 

237977 

58 

3 

699026 

3 - 6 f 

937312 

1-22 

762314 

4-86 

237686 

67 

4 

699844 

3 • o 3 

937238 

1-22 

762606 

4 • 85 

537394 

56 

5 

700062 

3-63 

937165 

1-22 

762897 

4 • 85 

237103 

55 

6 

700280 

3-63 

937092 

1-22 

763188 

4-85 

236812 

54 

7 

700498 

3-63 

937019 

1-22 

763409 

4-85 

236521 

53 

8 

700716 

3-63 

936946 

936872 

I • 22 

763770 

4-85 

23623 o 

52 

9 

700933 

3-62 

1-22 

764061 

4-85 

230939 

235648 

5 i 

IO 

70ii5i 

3-62 

936799 

1-22 

764352 

4-84 

5 o 

ii 

9-701368 

3-62 

9-936726 

1-22 

9-764643 

4.84 

10-235357 

49 

12 

70 i 585 

3-62 

936602 

1-23 

764933 

4-84 

235067 

48 

i 3 

701802 

3 - 6 i 

936578 

I -23 

766224 

4-84 

234776 

47 

14 

702019 

3 -61 

9365 o 5 

1-23 

765514 

4-84 

234486 

46 

i 5 

702236 

3 - 6 i 

93643i 

1-23 

760805 

4-84 

234195 

45 

16 

702462 

3 * 6 i 

936357 

1-23 

766095 

4-84 

233900 

44 

17 

702669 

702880 

3 -6o 

936284 

I -23 

766385 

4-83 

2336i5 

43 

18 

3 - 6 o 

936210 

1-23 

766676 

4-83 

233325 

42 

*9 

7o3ioi 

3 ’60 

936 1 36 

1-23 

766965 

4-83 

233o35 

41 

20 

703317 

3 -60 

936062 

1-23 

767206 

4*83 

232745 

40 

21 

9 ’ 7 o 3533 

3 - 5 9 

9-935988 

1-23 

9-767545 

4-83 

10-232455 

3 9 

22 

703749 

3’59 

935914 

g 3584 o 

1-23 

767834 

4-83 

232166 

38 

23 

703964 

3.59 

1-23 

768124 

4-82 

231876 

37 

24 

704179 

3-69 

980766 

1-24 

768413 

4-82 

23 1587 

36 

25 

704395 

3 . 5 9 

935692 

1-24 

768703 

4-82 

231297 

35 

26 

704610 

3-58 

986618 

1-24 

768992 

769281 

4-82 

23ioo8 

34 

7 1 

704825 

3’58 

935543 

1-24 

4-82 

230719 

33 

28 

705040 

3-58 

935469 

935390 

1-24 

769670 

4-82 

23o43o 

32 

=9 

7 o 5254 

3-58 

1-24 

769860 

4-8i 

23oi4o 

3 i 

3 o 

706469 

3-57 

935320 

1-24 

770148 

4-8i 

229862 

3 o 

3 1 

9’7o5683 

3-57 

9-936246 

1-24 

9-770437 

4-8i 

10-229563 

29 

32 

700898 

3-57 

935171 

1-24 

770726 

4 -81 

229274 

228985 

28 

33 

706112 

3 • 67 

935097 

1-24 

771015 

4-8i 

27 

34 

706326 

3-56 

g35o22 

1-24 

77i3o3 

4 • 81 

228697 

26 

35 

706539 

3-56 

934948 

1-24 

77^92 

4-8i 

228408 

25 

36 

706753 

3-56 

934873 

1-24 

771880 

4* 80 

228120 

24 

37 

706967 

3-56 

934798 

1-25 

772168 

4-80 

227832 

23 

38 

707180 

3-55 

934723 

1-25 

772457 

4-So 

227643 

22 

3 9 

707393 

3-55 

934649 

1-25 

772745 

4-80 

227255 

21 

40 

707606 

3-55 

934574 

1-25 

773o33 

4’8o 

226967 

20 

41 

9.707819 

3-55 

9-934499 

I -25 

9-773321 

4-8o 

10-226679 

IO 

42 

708032 

3-54 

934424 

1-25 

773608 

4-79 

226392 

10 

43 

708245 

3-54 

934349 

1-25 

773896 

4-79 

226104 

17 

44 

708458 

3-54 

934274 

I -25 

774184 

4-79 

225 Sl 6 

IO 

43 

708670 

3’54 

934199 

1-25 

774 -» 7 i 

4-79 

226629 

i 5 

46 

708882 

3-53 

934123 

1-25 

774759 

4-79 

225241 

14 

47 

709094 

3-53 

934048 

1-25 

775046 

4-79 

224954 

i 3 

48 

709306 

3-53 

933972 

933898 

1-25 

775333 

4-79 

224667 

12 

49 

709618 

3-53 

1-26 

775621 

4-78 

224379 

11 

5 o 

709730 

3-53 

933822 

I • 26 

776908 

4-78 

224092 

io 

5 i 

9-709941 

3-52 

9-933747 

1-26 

9-776195 

4-78 

io- 2238 o 5 

Q 

52 

7ioi53 

3*52 

933671 

1-26 

776482 

4-78 

2235 18 

8 

53 

7 io 364 

3-52 

933596 

1-26 

776769 

4-78 

22323I 

7 

54 

710575 

3-52 

933520 

1-26 

777 ° 5 o 

4-78 

222940 

6 

55 

710786 

3 - 5 i 

933445 

1-26 

777342 

4-78 

222658 

5 

56 

710997 

711208 

3 - 5 i 

3 - 5 1 

933369 

933290 

1-26 

1-26 

777628 

7779^5 

4-77 

4-77 

222372 

222085 

4 

3 

58 

J9 

71U19 

3 - 5 i 

933217 

1-26 

778201 

4-77 

221799 

2 

711629 

3 - 5 o 

933i4i 

1-26 

778487 

4-77 

22 l 5 l 2 

1 

60 

711839 

3 - 5 o 

933o66 

1-26 

778774 

4-77 

221226 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(59 DEGREES.) 








































SINES AND TANGENTS. (31 DEGREES.) 49 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9*711839 

3 * 5 o 

9*933o66 

1*26 

9-778774 

4*77 

10*221226 

60 

i 

7 I 2 o 5 o 

3 * 5 o 

932990 

1 • 27 

779060 

4-77 

220940 

59 

7 

712260 

3 * 5 o 

932914 

1*27 

779-846 

4 • 76 

220604 

58 

3 

712469 

3*49 

932838 

1*27 

779532 

4-76 

220868 

57 

4 

712679 

3*49 

932762 

1*27 

7799*8 

4*76 

220082 

56 

5 

712889 

3*49 

932686 

1 *27 

780203 

4*76 

219797 

55 

6 

718098 

3*49 

932609 

1 • 27 

780489 

4*76 

219611 

54 

1 

7i33o8 

3 *49 

932533 

1*27 

780775 

4 * 7 6 

219225 

53 

8 

713517 

3*48 

932457 

1*27 

781060 

4*76 

218940 

52 

9 

713726 

3 • 48 

93238 o 

1*27 

781346 

4*75 

218654 

5 i 

IC 

713935 

3*48 

9323 o 4 

1*27 

781631 

4*75 

218869 

5 o 

n 

9 * 7 i 4 i 44 

3*48 

9*932228 

1*27 

9*781916 

4*75 

10*218084 

40 

12 

714352 

3*47 

9321 5 i 

1*27 

782201 

4*75 

217799 

48 

i 3 

714561 

3*47 

932075 

1*28 

782486 

4*75 

217614 

47 

U 

714769 

3*47 

931998 

1*28 

782771 

4*75 

217229 

46 

i 5 

714978 

3*47 

931921 

1*28 

783 o 56 

4*75 

216944 

45 

16 

7i 5 i 86 

3*47 

93 i 845 

I *28 

783341 

4*75 

216659 

44 

17 

7 i 5394 

3*46 

931768 

1*28 

783626 

4*74 

216374 

43 

18 

716602 

3*46 

931691 

1*28 

783910 

4*74 

216090 

42 

19 

715809 

3*46 

931614 

1*28 

784195 

4-74 

2 i 58 o 5 

4 i 

20 

716017 

3 • 46 

931 537 

1*28 

784479 

4*74 

21 55 ?1 

40 

21 

9*716224 

3 *45 

9 * 93 i 46 o 

I *28 

9-784764 

4*74 

io* 2 i 5236 

39 

22 

716432 

3*45 

9 3 1 383 

1*28 

785048 

4-74 

214902 

38 

23 

716639 

3*45 

93 i 3 o 6 

1*28 

785332 

4*73 

214668 

37 

24 

716846 

3*45 

931229 

I *29 

7856 i 6 

4-73 

214384 

36 

25 

717053 

3 *45 

931152 

1*29 

785900 

4*73 

214100 

35 

26 

717259 

3*44 

931075 

I *29 

786!84 

4-73 

21 38 16 

34 

27 

717466 

3*44 

930998 

1*29 

786468 

4-73 

21 353 2 

33 

28 

7 1 7673 

3*44 

930921 

I • 29 

786752 

4*73 

213248 

32 

29 

717879 

3*44 

930843 

I *29 

787036 

4*73 

2i2964 

3 i 

3 o 

718085 

3 *48 

930766 

1*29 

787319 

4*72 

212681 

3 o 

3 i 

9*718291 

3*43 

9*930688 

1*29 

9*787603 

4*72 

10*212397 

29 

32 

718497 

3*43 

930611 

1*29 

787886 

4*72 

212114 

28 

33 

718708 

3*43 

93 o 533 

1*29 

788170 

4*72 

21i 83 o 

27 

34 

718909 

3 • 43 

93 o 456 

I *29 

788453 

4-72 

211 547 

26 

35 

719114 

3*42 

930378 

I • 29 

788736 

4-72 

211264 

25 

36 

719320 

3 • 42 

93 o 3 oo 

1 * 3 o 

789019 

4-72 

210981 

24 

h 

719525 

3 *42 

93 o 223 

1 * 3 o 

789302 

4*71 

210698 

23 

38 

719730 

3 • 42 

93 oi 45 

1 *3o 

789085 

4*71 

21041 5 

22 

3 9 

719935 

3 • 41 

930067 

i* 3 o 

789868 

4 * 7 * 

2101 3 2 

21 

4 o 

720140 

3 * 4 i 

929989 

1 * 3 o 

7901 5 1 

4*71 

209849 

20 

4 i 

9 * 72 o 345 

3 * 4 i 

9-929911 

1 * 3 o 

9*790433 

4*71 

10*209567 

19 

42 

720549 

3 * 4 i 

929833 

1 * 3 o 

790716 

4*71 

209284 

l8 

43 

720784 

3 * 4 o 

929755 

1 *3o 

790999 

4*71 

209001 

17 

44 

720958 

3 * 4 o 

929677 

1 *3o 

791281 

4*71 

208719 

l6 

45 

721162 

3 • 4 o 

929599 

1 * 3 o 

791 563 

4*70 

208437 

i 5 

46 

72 j 366 

3 * 4 o 

929521 

1 * 3 o 

791846 

4*70 

208154 

14 

47 

721570 

3 *4o 

929442 

1 * 3 o 

792128 

4*70 

207872 

i 3 

48 

721774 

3*39 

929364 

1 • 3 1 

792410 

4*70 

207590 

12 

4 ? 

721978 

3 * 3 9 

929286 

1 • 3 1 

792692 

4*70 

207308 

11 

5 o 

722181 

3 * 3 9 

929207 

1 • 3 1 

792974 

4*70 

207026 

10 

5 i 

9*722385 

3*39 

9*929129 

1 * 3 i 

9*793256 

4*70 

10*206744 

9 

52 

722588 

3 . 3 o 

92 oo 5 o 

1 - 3 1 

793538 

4*69 

206462 

0 

53 

722791 

3*38 

928972 

1 * 3 i 

793819 

4*69 

206181 

7 

54 

722994 

3*38 

928893 

1 - 3 1 

794101 

4*69 

205899 

6 

55 

723197 

3*38 

928815 

1 » 3 i 

794383 

4*69 

205617 

5 

56 

723400 

3*38 

928736 

1 * 3 i 

794664 

4*69 

2 o 5336 

4 

5 ? 

7236 o 3 

3*37 

928657 

1 * 3 i 

794945 

4*69 

2 o 5 o 55 

3 

58 

7238 o 5 

3*37 

928578 

1 * 3 i 

795227 

4.60 

204773 

2 

5 9 

724007 

3*37 

928499 

1 * 3 i 

7955 o 8 

4*68 

204492 

1 

60 

724210 

3.37 

928420 

1 * 3 i 

795789 

4*68 

204211 

c 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 


11 . 


(58 DEGREES.) 





































50 (32 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-724210 

3-37 

9-928420 

I -32 

9.795789 

4-68 

10-204211 

60 

i 

724412 

3-37 

928342 

1-32 j 

796070 

4-68 

203930 

5 9 

2 

724614 

3-36 

928263 

1-32 

796381 

4-68 

203649 

58 

3 

724816 

3-36 

928183 

1-32 

796632 

4-68 

2o3368 

57 

4 

726017 

3-36 

928104 

1-32 

796913 

4-68 

203087 

56 

5 

726219 

3-36 

928025 

1-32 

797'94 

4-68 

202806 

55 

6 

726420 

3-35 

927946 

1-32 

797475 

4-68 

202525 

54 


72 562 2 

3-35 

927867 

I -32 

797755 

4-68 

202245 

53 

9 

725823 

726024 

3-35 

3-35 

927787 

927708 

1-32 

1-32 

798036 

798316 

4-67 

4-67 

201964 

201684 

52 

5i 

10 

726225 

3 - 3 d 

927629 

I -32 

798696 

4-67 

201404 

5o 

11 

9-726426 

3-34 

9-927549 

1-32 

9-798877 

4-67 

10-201123 

49 

I 2 

726626 

3-34 

927470 

1-33 

799157 

4-67 

200843 

48 

i3 

726827 

3-34 

927390 

i *33 

799437 

4-67 

2 oo 563 

47 

i 4 

727027 

3-34 

927310 

i -33 

799717 

4-67 

200283 

46 

i 5 

727228 

3-34 

927231 

i -33 

799997 

4-66 

200003 

45 

16 

727428 

3-33 

927151 

i -33 

800277 

4-66 

199723 

44 

17 

727628 

3-33 

927071 

i -33 

800667 

4-66 

199443 

43 

18 

727828 

3-33 

926991 

i -33 

8 oo 836 

4-66 

199164 

198884 

42 

19 

728027 

3-33 

926911 

i -33 

801116 

4-66 

41 

20 

728227 

3-33 

92683i 

i -33 

801396 

4-66 

198604 

40 

21 

9-728427 

3-32 

9-926751 

i -33 

9-801675 

4-66 

10-198325 

3 9 

22 

728626 

3-32 

926671 

i -33 

801965 

4-66 

198045 

38 

23 

728825 

3-32 

926591 

i -33 

802234 

4-65 

197766 

37 

24 

729024 

3-32 

926511 

i -34 

8o25i3 

4-65 

197487 

36 

2D 

729223 

3 - 3 1 

926431 

i -34 

802792 

4-65 

197208 

35 

26 

729422 

3 - 3 1 

92635i 

i -34 

803072 

4-65 

196928 

34 

27 

729621 

3 • 3 1 

926270 

1 • 34 

8 o 335 i 

4-65 

196649 

33 

28 

729820 

3 • 3 1 

926190 

1-34 

8 o 363 o 

4-65 

196370 

32 

29 

730018 

3 - 3 o 

926110 

i -34 

803908 

4-65 

196092 

3i 

3 o 

730216 

3 - 3 o 

926029 

i -34 

804187 

4-65 

I958i3 

3o 

3 1 

32 

9-”73o4i5 
73o613 

3 - 3 o 

3 - 3 o 

9-925949 

025868 

i -?4 

i -4 

9•804466 
804745 

4-64 

4-64 

10-195534 
195255 

20 

28 

33 

73o8i1 

3 - 3 o 

926788 

1-34 

8o5o23 

4-64 

194977 

27 

34 

731009 

3 • 29 

925707 

1 -34 

8o53o2 

4-64 

194698 

26 

35 

731206 

3 • 29 

925626 

1 -34 

8o558o 

4-64 

194420 

26 

36 

73i4o4 

3-29 

925545 

i -35 

8o5859 

4-64 

194141 

24 

37 

73i6o2 

3 • 29 

925465 

i -35 

806137 

4-64 

193863 

23 

38 

731799 

3 • 29 

925384 

i -35 

80641 3 

4-63 

193535 

22 

39 

731996 

3-28 

9253o3 

1 -35 

806693 

4-63 

193307 

21 

40 

732193 

3-28 

925222 

i -35 

806971 

4-63 

193029 

20 

4 i 

9-732390 

732587 

3-28 

9 - 925141 

i -35 

9-807249 

4-63 

10-192751 

19 

42 

3-28 

925o6o 

i -35 

807527 

4-63 

192473 

l8 

43 

732784 

3-28 

924979 

i -35 

807806 

4-63 

192195 

17 

44 

732980 

3-27 

924897 

1 -35 

8 o 8 o 83 

4-63 

191917 

l6 

45 

733177 

3-27 

924816 

i -35 

8 o 836 i 

4-63 

191639 

i 5 

46 

733373 

3-27 

924785 

i -36 

8 o 8638 

4-62 

191362 

14 

47 

733560 

3-27 

924654 

i -36 

808916 

4-62 

191084 

i 3 

48 

73376D 

3-27 

924572 

1 -36 

809193 

4-62 

190807 

12 

49 

733961 

3.26 

92449 1 

i -36 

809471 

4-62 

190529 

11 

5o 

734i57 

3 • 26 

924409 

i -36 

809748 

4-62 

190252 

10 

5i 

9-734353 

3 • 26 

9-924328 

i -36 

9-810025 

4-62 

10-189975 

Q 

52 

734549 

3-26 

924246 

i -36 

8io3o2 

4-62 

IS9698 

8 

53 

734744 

3-25 

924164 

1 -36 

8 io 58 o 

4-62 

189420 

'*£ 

54 

734939 

3-25 

924083 

i -36 

810857 

4-62 

189143 

6 

55 

735 i 35 

3-25 

924001 

i -36 

8 i11 34 

4-6i 

188866 

5 

56 

73533o 

3-25 

923919 

i -36 

811410 

4-6i 

188590 

4 

57 

735525 

3-25 

923837 

i -36 

811687 

4 - 6 t 

1 883 i 3 

3 

58 

735719 

3*24 

923755 

i-3 7 

811964 

4-6i 

i 88 o 36 

2 

59 

735914 

3-24 

923673 

1-37 

812241 

4-6i 

187759 

i 8 7 483 

1 

60 

736109 

3-24 

923691 

i-3 7 

812517 

4-6i 

0 

1_ 

Cosine 

D. 

Sine 

1 D. 

Cotang. 

D. 

Tang. 

M. 


(57 DEGREES.) 






















































SINES AND TANGENTS. (33 DEGREES.) 


51 


' 

M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-736109 

7363 o 3 

3-24 

9-923591 

1-37 

9• S 1 25 17 

4-6i 

10-187482 

60 

i 

3-24 

923509 

1-37 

812794 

4-6i 

187206 

5 q 

2 

736498 

3-24 

923427 

1 - 3 i 

813070 

4-6i 

186930 

58 

3 

736692 

736886 

3-23 

923346 

1-37 

8 i 3347 

4-60 

186653 

57 

4 

3-23 

923263 

1-37 

8 i 3623 

4-60 

186377 

56 

5 

737080 

3-23 

923181 

1.37 

813899 

4-60 

186101 

55 

6 

737274 

3-23 

923098 

1-37 

814175 

4-6c 

186822 

54 

7 

737467 

3-23 

923016 

1-37 

814452 

4- 60 

186648 

53 

8 

737661 

3-22 

922933 

922861 

i *3 7 

814728 

4-60 

186272 

52 

9 

737855 

3-22 

i- 3 7 

816004 

4-60 

184996 

5 i 

10 

738048 

3-22 

922768 

i -38 

816279 

4-60 

184721 

5 o 

ii 

9-738241 

3-22 

9-922686 

i -38 

9-81 5555 

4-59 

10•1 84445 

49 

12 

738434 

3-22 

922603 

1-38 

81 583 1 

4 - 5 g 

184169 

48 

i 3 

738627 

8-21 

922620 

i -38 

816107 

4-59 

i 838 9 3 

47 

14 

738820 

3-21 

922438 

i -38 

8 i 6382 

4 - 5 g 

1 836 18 

46 

i 5 

739013 

3-21 

922355 

i -38 

81 6658 

4 - 5 g 

183342 

45 

16 

739206 

3-21 

922272 

i -38 

816933 

4 - 5 g 

183067 

44 

17 

739398 

3-21 

922189 

i -38 

817209 

4 - 5 g 

182791 

43 

18 

739690 

3-20 

922106 

i -38 

817484 

4-69 

182616 

42 

»9 

739783 

3-20 

922023 

i -38 

817769 

4-59 

182241 

41 

20 

739975 

3-20 

921940 

i -38 

8 i 8 o 3 d 

4-58 

181965 

40 

21 

9-740167 

3-20 

9-921857 

1-39 

9-81 83 10 

4-58 

io-181690 

3 9 

22 

740359 

3-20 

9 21 774 

1 *39 

81 8585 

4-58 

18141 5 

38 

23 

74o55o 

3 -19 

921691 

1 -39 

818860 

4-58 

181140 

37 

24 

740742 

3 -19 

921607 

1-39 

819135 

4-58 

180865 

36 

2D 

740934 

3 • 19 

921524 

1 -39 

819410 

4-58 

180690 

35 

26 

741125 

3*19 

921441 

1 *39 

819684 

4-58 

1 8 o 3 16 

3 i 

27 

741 3 16 

3-19 

921357 

1-39 

819969 

4-58 

180041 

33 

28 

741608 

3 -18 

921274 

1 - 3 g 

820234 

4-58 

179766 

3 s 

29 

741699 

3 -18 

921190 

1 -39 

82 o 5 o 8 

4.57 

179492 

3 i 

3 o 

741889 

3 -18 

921107 

1 • 3 g 

820783 

4-67 

179217 

3 o 

3 i 

9-742080 

3 -18 

9-921023 

1 -39 

9-821057 

4-57 

10-178943 

2 9 

32 

742271 

3 -18 

920939 

920866 

1 - 4 o 

82 i 332 

4-57 

178668 

28 

33 

742462 

3-17 

1 - 4 o 

821606 

4.67 

178394 

27 

34 

742662 

3-17 

920772 

1 - 4 o 

821880 

4.57 

178120 

26 

35 

742842 

3-17 

920688 

1 - 4 o 

822 i 54 

4.57 

177846 

25 

36 

743 o 33 

3-17 

920604 

1 - 4 o 

822429 

4.57 

177571 

24 

37 

743223 

3-17 

920520 

1 - 4 o 

822703 

4.57 

177297 

23 

38 

7434 i 3 

3 -16 

920436 

1 -4o 

822977 

4-56 

177023 

22 

39 

743602 

3 -16 

920362 

1 - 4 o 

823250 

4-56 

176760 

21 

4 o 

743792 

3 -16 

920268 

1 - 4 o 

823524 

4-56 

176476 

20 

4 i 

9-743982 

3 -i 6 

9-920184 

1 - 4 o 

9-823798 

4-56 

10-176202 


42 

74417 1 

3 -i 6 

920099 

1 - 4 o 

824072 

4-56 

175928 

l8 

43 

74436 i 

3 • 1 5 

920015 

1 - 4 o 

824345 

4-56 

175655 

17 

44 

74455o 

3 • 1 5 

919931 

1 • 4 1 

824619 

4-56 

i 7 538 i 

l6- 

45 

46 

74473 q 

744928 

3 • 1 5 

3 -1 5 

919846 

919762 

1 - 4 * 

1 • 4 1 

82489) 

826166 

4-56 

4-56 

175107 

174834 

id 

i 4 . 

47 

746117 

3 -1 5 

919677 

i- 4 i 

825439 

4-55 

174661 

1) 

43 

7453o6 

3 -i 4 

919593 

1 * 4 i 

82671) 

4-55 

174287 

12 

49 

745494 

3 -i 4 

919508 

1 - 4 i 

826986 

4-55 

174014 

in 

5 o 

745683 

3 -i 4 

919424 

1 - 4 i 

826269 

4-55 

173741 

10 

5 i 

9-745871 

3 -14 

9-919339 

1 - 4 i 

9-826532 

4-55 

10-173468 

9 

52 

746059 

3 -14 

919254 

1 - 4 i 

826806 

4-55 

173195 

8 

53 

746248 

3 • i 3 

919169 

i- 4 i 

827078 

4-55 

172922 

7 

54 

746436 

4-13 

919086 

1 * 4 i 

827351 

4-55 

172649 

6 

55 

746624 

3 • i 3 

919000 

1 * 4 i 

827624 

4-55 

172376 

5 

56 

746812 

3-13 

918915 

918830 

918745 

1-42 

827897 

4 • 54 

172103 

4 

57 

58 

746909 

747187 

3 • 1 3 
3-12 

1-42 

1-42 

828170 

828442 

4-54 

4-54 

171830 

I 7 i 558 

3 

2 

59 

747374 

3-12 

918669 

1-42 

828715 

4-54 

171285 

1 

60 

747562 

3-12 

918574 

1 -42 

828987 

4-54 

171013 

0 

_ 

Coeine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 



18 (56 DEGREES.) 




















































52 (34 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-747662 

3-12 

9-918574 

1 -42 

9-828987 

4.54 

io-171013 

60 

i 

747749 

3-12 

918489 

1-42 

829260 

4-54 

170740 

5 9 

a 

747936 

3-12 

918404 

1 -42 

829532 

4-54 

170468 

58 

3 

748123 

3-i 1 

918318 

1-42 

829805 

4-54 

170195 

57 

4 

748310 

3-n 

918233 

I -42 

830077 

4*54 

169923 

56 

5 

748497 

3-11 

918147 

1-42 

83o349 

4-53 

169651 

55 

6 

748683 

3-11 

918062 

1-42 

83o62i 

4-53 

169379 

54 

n 

748870 

749066 

3-n 

917976 

1 -4 3 

83o8g3 

4-53 

169107 

53 

8 

3-10 

917891 

1 -43 

831i65 

4-53 

168835 

52 

9 

749243 

3-io 

917805 

1 -43 

83i437 

4-53 

168563 

5i 

IO 

749429 

3-io 

9X7719 

1 -43 

831709 

4-53 

168291 

5o 

11 

9-7496i5 

3-io 

9-917634 

1 -43 

9-831981 

4-53 

10-168019 

49 

12 

i3 

749801 

749987 

3-io 

3-09 

917548 

917462 

1 -43 

1 -43 

832253 

832525 

4-53 

4 - 53 

167747 

167475 

48 

47 

14 

760172 

3*09 

917376 

1 -43 

832796 

4-53 

167204 

46 

|5 

75o358 

3-og 

917290 

1 -43 

833o68 

4-52 

166932 

45 

16 

75o543 

3-09 

917204 

1 -43 

833339 

4-52 

166661 

44 

17 

760729 

3-09 

917118 

1 -44 

833611 

4-52 

166389 

43 

18 

760914 

3-o8 

917032 

1-44 

833882 

4-52 

166118 

42 

19 

761099 

3-08 

916046 

i-44 

834i54 

4-52 

166846 

4i 

20 

751284 

3-08 

916859 

i-44 

834425 

4-52 

166675 

4o 

21 

9-751469 

3-08 

9-916773 

1-44 

9•834696 

4-52 

io- i653o4 

39 

22 

761654 

3-08 

916687 

i-44 

834967 

835238 

4-52 

i65o33 

38 

23 

761839 

3- 08 

916600 

1 -44 

4-52 

164762 

37 

24 

762023 

3-07 

916514 

1-44 

835509 

4-52 

164491 

36 

25 

762208 

3-07 

916427 

i-44 

835780 

4-5i 

164220 

35 

26 

27 

762392 

762676 

3-07 

3-07 

916341 

916254 

1 -44 

1 -44 

836o5i 

836322 

4 • 5 i 

4 - 51 

163949 

163678 

34 

33 

28 

762760 

3-07 

916167 

1 -45 

836693 

836864 

4 • 51 

163407 

32 

29 

752944 

3-06 

916081 

1 -45 

4 • 51 

163136 

3i 

3o 

753128 

3-06 

915994 

1 -45 

837134 

4-5i 

162866 

3o 

3i 

9-763312 

3-06 

9-9I5907 

915820 

1 -45 

9-8374o5 

4-5i 

io-162595 

29 

32 

763495 

3-o6 

1 -45 

837675 

4 • 51 

162325 

28 

33 

763679 

3-o6 

9i5733 

1 -45 

837946 

838216 

4 - 5i 

162054 

27 

34 

753862 

3-o5 

916646 

1 -45 

4 • 51 

161784 

26 

35 

764046 

3-o5 

915559 

1 -45 

838487 

4-5o 

161513 

25 

36 

754229 

3-o5 

qi5472 

1 -45 

838757 

4-5o 

161243 

24 

37 

754412 

3-o5 

9 i5385 

1 -45 

839027 

4-5o 

160973 

23 

38 

764596 

3-o5 

915297 

1 -45 

839297 

839668 

4-5o 

160703 

22 

39 

754778 

3-04 

915210 

1 -45 

4-5o 

160432 

21 

40 

764960 

3-o4 

915123 

1 -46 

83g838 

4-5o 

160162 

20 

4i 

9-755i43 

3-o4 

0-gi5o35 

1 -46 

9-840108 

4-5o 

10-159892 

19 

42 

755326 

3-o4 

914948 

1 -46 

840378 

4-5o 

159622 

18 

43 

7555o8 

3-04 

914860 

1 -46 

840647 

4-5o 

15g353 

17 

44 

755690 

3-o4 

91477 3 

1 -46 

840917 

4.49 

159083 

158813 

16 

45 

755872 

3-o3 

914685 

1 -46 

841187 

4.49 

i5 

46 

756o54 

3-o3 

914598 

1 -46 

841457 

4-49 

158543 

14 

47 

756236 

3-o3 

914510 

1 -46 

841726 

4-49 

168274 

i3 

48 

766418 

3-o3 

914422 

1 -46 

841996 

4.49 

i58oo4 

12 

49 

756600 

3-o3 

914334 

1 -46 

842266 

4.49 

167734 

11 

5o 

766782 

3-02 

914246 

i-47 

842535 

4.49 

157460 

10 

5i 

9-756963 

3-02 

9-914158 

i-47 

9 842805 

4-49 

io-157195 

9 

52 

757144 

3-02 

914070 

1-47 

843074 

4-49 

156926 

8 

53 

767326 

3-02 

913982 

1-47 

843343 

4-49 

156657 

7 

54 

757507 

3-02 

913894 

1-47 

843612 

4-49 

i56388 

6 

55 

757688 

3-oi 

913806 

1-47 

843882 

4-48 

i56118 

5 

56 

757869 

3-oi 

913718 

1-47 

844151 

4-4? 

155849 

4 

5 l 

758o5o 

3-oi 

9i363o 

1-47 

844420 

4-48 

i5558o 

3 

58 

69 

75823o 

3-oi 

9i354i 

J-47 

844689 

4-48 

155311 

2 

7584 i1 

3-oi 

9i3453 

1-47 

844968 

4-48 

i55o42 

f 

60 

758591 

3-oi 

913365 

1-47 

846227 

. 

4-48 

154773 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

1 M. 


(55 DEGREES.) 





















































SINES AND TANGENTS. (35 DEGREES.) 


53 


M. 

Sine 

D. 

Cosine 

D. 

rang. 

D. 

Cotang. 


0 

9-758591 

3 *oi 

9*91 3365 

i *47 

9*846227 

4-48 

10*154773 

60 

E 

738772 

3 *oo 

913276 

1-47 

845496 

4*48 

1 545 o 4 

59 

t 

75S9T2 

3 -oo 

913187 

1-48 

843764 

4-48 

1 54236 

58 

3 

769132 

3 -oo 

9130919 

1 *48 

846 o 33 

4 48 

153967 

57 

4 

769312 

3 -oo 

9i3oio 

1 *48 

846302 

4.48 

163698 

56 

5 

769492 

3 -oo 

912833 

1*48 

846370 

4-47 

1 5343 o 

55 

6 

739672 

2*99 

1 *48 

846889 

4-47 

1 53 16i 

54 

7 

769852 

2*99 

912744 

1 *48 

847107 

4*47 

162893 

53 

8 

760031 

2*99 

912655 

1 *48 

847376 

4*47 

162624 

52 

9 

760211 

2*99 

912666 

1 *48 

847644 

4-47 

152356 

5 i 

10 

760390 

2*99 

912477 

1 *48 

847913 

4-47 

152087 

5 o 

ii 

9*760669 

2*98 

9 *912388 

1 *48 

9*848181 

4*47 

io* 551819 

49 

i 12 

760748 

2 *98 

912299 

1*49 

848449 

4-47 

i 5 i 55 i 

48 

! i 3 

760927 

2 *98 

912210 

1-49 

848717 

4-47 

1 5 i 283 

47 ! 

14 

761106 

2*98 

912121 

i- 4 g 

848986 

4.47 

i 5 ioi 4 

46 

i 5 

761285 

2 *98 

gi2o3i 

1*49 

849254 

4*47 

150746 

45 

16 

761464 

2*98 

911942 

1*49 

849522 

4.47 

150478 

44 

1 *7 
18 

761642 

2*97 

911 853 

1 *49 

849790 

4.46 

l 5 o 2 IO 

43 

761821 

2*97 

911763 

1*49 

85 oo 58 

4*46 

149943 

42 

I 19 

761999 

2*97 

911674 

1*49 

85 o 325 

4*46 

149676 

41 

20 

762177 

2*97 

911 584 

1*49 

860393 

4*46 

149407 

40 

i 21 

9*762356 

2*97 

9*911495 

1*49 

9 * 85 o 86 i 

4*46 

10*149139 

3 g 

*22 

762534 

2 *96 

91t 4 o 5 

1 *49 

85 1129 

4.46 

148871 

38 

23 

762712 

762889 

2*96 

91 i 3 i 5 

1 * 5 o 

861396 

4*46 

148604 

3 ; 

24 

2 *96 

911226 

r * 5 o 

851664 

4*46 

148336 

36 

25 

763067 

2 *96 

9 in 36 

1 * 5 o 

85 iq 3 i 

4-46 

148069 

35 

26 

763245 

2 *96 

911046 

1 * 5 o 

862199 

4.46 

147801 

34 

: 27 

763422 

2-96 

910966 

i* 5 o 

852466 

4 • 46 

147534 

33 i 

28 

763600 

2 *95 

91086& 

i* 5 o 

862733 

4*45 

147267 

32 

29 

763777 

2 *95 

910776 

1 * 5 o 

853 ooi 

4*45 

146999 

146782 

3 i 

! 3© 

763964 

2*95 

910686 

1 * 5 o 

853268 

4-45 

3 o 

! 3 ! 

9 *- 64 i 3 f 

764308 

2 *96 

Q* 9 io 5 g 6 

1 * 5 o 

9*853535 

4*45 

10*146465 

29 

, 32 

2*95 

910606 

1 * 5 o 

853802 

4*45 

146198 

28 

33 

764485 

2*94 

91041 5 

1 * 5 o 

854069 

4*45 

140931 

27 

' 34 

764662 

2*94 

910826 

1 * 5 i 

854336 

4*45 

145664 

26 

i 35 

764838 

2*94 

910235 

i* 5 i 

8546 o 3 

4*45 

145397 

23 

36 

766015 

2*94 

910144 

1 * 5 i 

854870 

4*45 

140180 

24 

3 ? 

765191 

2* g 4 

910064 

1 * 5 i 

855 i 37 

4*45 

144863 

23 

38 

765367 

2-94 

909963 

1 * 5 i 

8554 o 4 

4*45 

144096 

22 

3 g 

760044 

2 * 98 

909873 

1 * 5 i 

855671 

4*44 

144329 

21 

i 4 © 

765720 

2 -93 

909782 

1 * 5 i 

855 9 38 

4*44 

144062 

20 ! 

4 i 

9*766896 

2 -93 

9*909691 

i* 5 i 

9*866204 

4*44 

10*148796 

IO 

42 

766072 

2 *93 

909601 

1 - 5 i 

85647 1 

4*44 

143029 

IS 

43 

766247 

2*98 

909610 

i * 5 i 

856 7 3 7 

4*44 

143263 

17 

44 

45 

766423 

766698 

2 *98 
2*92 

909419 

909328 

1 * 5 i 
1*62 

857004 

857270 

4*44 

4*44 

142996 

142700 

16 

IO 

46 

766774 

2*92 

909287 

1*52 

857537 

4*44 

142463 

14 

47 

766949 

2 *92 

9091 46 

1*52 

857803 

4*44 

142197 

i 3 

48 

767124 

2*92 

909066 
* 908964 

I • 52 

868069 

4*44 

141931 

12 

49 

7673010 

2*92 

i *5 2 

858336 

4*44 

141664 

11 

5 o 

767475 

2*91 

908873 

1*52 

858602 

4*43 

141398 

10 

5 ? 

g*767649 

2*91 

9*908781 

1*62 

9*858868 

4*43 

io*1411 3 a 

9 

5 s 

767824 

2*91 

908690 

1 * 5 ^ 

859134 

4*43 

140866 

8 

53 

767999 

2*91 

908699 

1*52 

859400 

4*43 

140600 

7 

54 

768173 

291 

908507 

1*62 

859666 

4*43 

i 4 o 334 

6 

55 

768348 

2-90 

908416 

i *53 

859932 

4*43 

140068 

5 

56 

768622 

2*90 

908324 

i *53 

860198 

4*43 

139802 

4 

57 

768697 

2-90 

908233 

i *53 

860464 

4*43 

139036 

3 

58 

768871 

2*90 

908141 

i *53 

860730 

4*43 

139270 

2 

5 9 

769046 

2*90 

908049 

i *53 

860996 

4*43 

i 3 qoo 5 

1 

60 

769219 

2*90 

907958 

i *53 

861261 

4*43 

138739 

0 

*T" 

L - 

Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(54 DEGREES.) 

































54 


(36 DEGREES.) A TABLE OF LOGARITHMIC? 


M. 

Sine 

D 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9.769219 

2-90 

9.907958 

1-53 

9-861261 

4.43 

io-138739 

60 

i 

769398 

2*89 

907866 

i-53 

861527 

4.43 

138473 

5y 

i 

769566 

2-89 

907774 

i-53 

861792 

4*42 

138208 

58 

3 

769740 

2-89 

907682 

i-53 

862068 

4-42 

137942 

1 ^7 

4 

769913 

2-89 

907590 

i-53 

862323 

4-42 

137677 

1 56 

5 

770087 

2-89 

907498 

1-53 

862089 

4-42 

13741 1 

55 

6 

770260 

2-88 

907406 

1 -53 

862854 

4-42 

137146 

54 

7 

770433 

2-88 

907314 

1-54 

863119 

4-42 

13688 1 

53 

8 

770606 

2-88 

907222 

1-54 

863385 

4*42 

i366i5 

52 

9 

770779 

2-88 

907129 

1*54 

86365o 

4.42 

i3635o 

5i 

10 

770952 

2-88 

907037 

i *54 

863915 

4-42 

i36o85 

5o 

ii 

9.771125 

2-88 

9.906945 

1*54 

9-864180 

4-42 

IO-135820 

49 

12 

771298 

2-87 

906852 

1.54 

864443 

4-42 

135555 

48 

i3 

771470 

2-87 

906760 

1*54 

864710 

4-42 

135290 

47 

14 

771643 

2-87 

906667 

1-54 

864975 

4-41 

i35o25 

46 

i5 

771815 

2-87 

906575 

1*54 

865240 

4-41 

134760 

45 

16 

771987 

2*87 

906482 

i *54 

8655o5 

4-41 

134495 

44 

17 

772169 

2-87 

906389 

i.55 

865770 

4-4i 

i 342.3 o 

43 

18 

77233 i 

2-86 

906296 

1*55 

866o35 

4-4J 

133965 

42 

19 

7725 o 3 

2-86 

906204 

i-55 

8663oo 

4-4i 

133700 

41 

20 

772675 

2-86 

906111 

i*55 

866564 

4.41 

133436 

40 

21 

9-772847 

2-86 

9-906018 

i-55 

9-866829 

441 

io-133171 

39 

22 

773018 

2-86 

905925 

i-55 

867094 

4*4i 

132906 

38 

23 

773190 

2-86 

9o5832 

1 55 

867358 

4*41 

132642 

3? 

24 

77336 i 

2*85 

9o573o 

1-55 

867623 

4-4i 

132377 

36 

25 

773533 

2-85 

905645 

1-55 

867887 

4-4i 

1321i3 

35 

26 

773704 

2-85 

905552 

i-55 

868152 

4.40 

131848 

34 

27 

773875 

2-85 

905469 

1-55 

868416 

4-4o 

1 31584 

33 

28 

774046 

2-85 

9 o 5366 

i-56 

868680 

4-4o 

i 3 i 32 o 

32 

29 

774217 

2-85 

905272 

1-56 

868945 

4-4o 

i 3 io 55 

3i 

3o 

774388 

2-84 

905179 

i>56 

869209 

4.40 

130794 

3o 

3i 

9-774558 

2-84 

9"9o5o85 

i-56 

9-869473 

4.40 

10.i3o527 

29 

32 

774729 

2-84 

904992 

1*56 

869737 

4-40 

i 3 o 263 

28 

33 

774899 

2-84 

904898 

1-56 

870001 

4-40 

129999 

27 

34 

775070 

2-84 

904804 

1-56 

870265 

4-4o 

129735 

26 

35 

775240 

2-84 

904711 

1*56 

870529 

4.40 

1 2947 1 

25 

35 

77 5 4 io 

2-83 

904617 

i*56 

870793 

4.40 

1 29207 

24 

37 

77558o 

2-83 

904523 

1 -56 

871057 

4.40 

1 28943 

23 

38 

775750 

2-83 

904429 

1*57 

871321 

4.40 

128679 

22 

3 9 

775920 

2-83 

90433 d 

i- 5 7 

87i585 

4.40 

128415 

21 

40 

776090 

2-83 

904241 

1.57 

871849 

4.39 

!28 i 5 i 

20 

4i 

9.776259 

2-83 

9-904147 

i- 5 7 

9-872112 

4.39 

10-127888 

IO 

42 

776429 

2-82 

9o4o53 

1-5-7 

872376 

4.39 

127624 

l 8 

43 

776598 

2-82 

903959 

1.57 

872640 

4.39 

127360 

17 

44 

776768 

2*82 

903864 

i- 5 7 

872903 

4-39 

127097 

16 

45 

770937 

2-82 

903770 

1 "67 

873167 

4.39 

126833 

i5 

46 

777106 

2-82 

908676 

1-5; 

873480 

4.39 

i26070 

• 4 

47 

777275 

2 • 81 

9o358i 

1 • 57 

873694 

4.39 

12 >806 

i3 

48 

777444 

2-81 

903487 

i- 5 7 

873957 

4.39 

125043 

12 

49 

777613 

2-81 

903392 

1-58 

874220 

4.39 

12D780 

11 

5o 

777781 

2 • 8l 

903298 

1-58 

874484 

4.39 

125516 

10 

5i 

9-777950 

2-8l 

9*9 o 32 o 3 

1-58 

9-874747 

4-39 

10-125253 

9 

52 

778119 

2*8l 

903108 

i-53 

875010 

4.39 

124990 

8 

53 

778287 

2-80 

9 o 3 oi 4 

i-58 

875273 

4-38 

124727 

7 1 

54 

778455 

2* 80 

902019 

i*58 

8 7 5536 

4-38 

1 24464 

6 | 

55 

778624 

2-80 

902824 

i-58 

875800 

4-38 

124200 

5 

55 

778792 

2-80 

902729 

i-58 

876063 

4-38 

1 28987 

4 

57 

778960 

2-80 

902634 

i-53 

876326 

4-38 

123674 

3 

58 

779128 

2-80 

902539 

1*59 

876589 

4-38 

123411 

2 

5 9 

779295 

2* ^9 

902444 

1*59 

876851 

4-38 

128149 

1 

60 

779463 

2.79 

902349 

1-69 

877114 

4-38 

122886 

0 


Coaine 

D. 

Sine 

D. 

Cotanw-. 

D. 

Tang 

M. 


(53 DEGREES.) 



























































SINES AND TANGENTS. (37 DEGREES.) 


55 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

o 

9.779463 

2-79 

9.902849 

1*59 

9-877114 

4-38 

10-122886 

i 

779631 

2.79 

Q 02253 

1.59 

877377 

4-38 

122623 

2 

779798 

2-79 

902158 

1.59 

877640 

4-38 

122360 

3 

779966 

2-79 

902063 

1*59 

877903 

4-38 

122097 

4 

78 oi 33 

2-79 

901967 

1 -69 

878165 

4-38 

I 2 i 835 

5 

78 o 3 oo 

2.78 

901872 

1.59 

878428 

4-38 

121572 

6 

780467 

2-78 

901776 

1*59 

878691 

4-38 

121309 

7 

780634 

2-78 

90168c 

1*59 

878953 

4-37 

121047 

8 

780801 

2-78 

901 586 

1*59 

879216 

4.37 

120784 

9 

780968 

2-78 

901490 

1 -69 

879478 

4-37 

120522 

io 

781i 34 

2-78 

901394 

1 -6o 

879741 

4-37 

120259 

K 

9-781301 

2.77 

9-901298 

1 -6o 

9-880003 

4.37 

10-I19997 

12 

781468 

2.77 

901202 

1 -6o 

88 o 265 

4-37 

119735 

i 3 

781634 

2.77 

901106 

1 -6o 

88 o 528 

4.37 

119472 

14 

781800 

2-77 

901010 

1 -60 

880790 

4-37 

119210 

i 5 

781966 

2-77 

90091 4 

1 -6o 

88 io 52 

4-37 

II8948 

16 

782132 

2-77 

000818 

1 -6o 

881 3 14 

4-37 

ii8686 

*7 

782298 

2-76 

900722 

1 -6o 

88 i 5 7 6 

4-37 

118424 

18 

782464 

2-76 

900626 

1 -6o 

88 i 83 9 

4-37 

11Bt 61 

l 9 

782630 

2-76 

900529 

1 -6o 

882101 

4.37 

117899 

20 

782796 

2-76 

900433 

1 • 61 

882363 

4-36 

117637 

21 

9.782961 

2-76 

9-900337 

1 -6i 

9-882625 

4-36 

10-117375 

22 

783127 

2-76 

900240 

1 -6i 

882887 

4-36 

117113 

23 

783292 

2-75 

900144 

1 -6i 

883148 

4-36 

11 6852 

24 

783408 

2*75 

900047 

1 -6i 

8834 io 

4-36 

116590 

25 

783623 

2-75 

899951 

1 -6i 

883672 

4-36 

116328 

26 

783788 

2*75 

899854 

i -6i 

883 9 34 

4-36 

116066 

27 

783953 

2*75 

899757 

1*61 

884196 

4-36 

11 58 o 4 

28 

784118 

2.75 

899660 

i -6i 

884407 

4-36 

ii 5543 

29 

784282 

2-74 

899564 

1 -6i 

884719 

4-36 

116281 

35 

784447 

2*74 

899467 

1 -62 

884980 

4-36 

Il 5 o 20 

3 i 

9.784612 

2*74 

9-899370 

1.62 

9-885242 

4-36 

10-I14758 

32 

784776 

2-74 

899273 

1 -62 

8855 o 3 

4-36 

114497 

33 

784941 

2-74 

899176 

1 -62 

886765 

4-36 

114235 

34 

785 io 5 

2-74 

899078 

1-62 

886026 

4-36 

I13974 

35 

785269 

2-73 

898981 

1 62 

886288 

4-36 

113712 

36 

785433 

2-73 

898884 

1 -62 

886549 

4-35 

I1345I 

37 

785597 

2*73 

898787 

1 -62 

886810 

4-35 

i13190 

38 

785761 

2-73 

898689 

1 -62 

887072 

4-35 

112928 

3 o 

785925 

2-73 

898692 

1-62 

887333 

4-35 

112667 

40 

786089 

2-73 

898494 

1-63 

887594 

4-35 

112406 

4i 

9.786252 

2-72 

9-898397 

i -63 

9-887855 

4*35 

10-112145 

42 

786416 

2-72 

898299 

1-63 

888116 

4-35 

111884 

43 

786579 

272 

898202 

i -63 

888377 

4-35 

1 11623 

44 

786742 

2-72 

898104 

i -63 

888639 

4-35 

11i 36 i 

45 

786906 

2-72 

898006 

i -63 

888900 

4-35 

111100 

46 

787069 

2-72 

897908 

i -63 

889160 

4-35 

110840 

47 

787232 

271 

897810 

i -63 

889421 

4-35 

110579 

4« 

787395 

2-71 

897712 

i -63 

889682 

4-35 

11o318 

49 

787557 

2-71 

897614 

i -63 

889943 

4-35 

110057 

5 o 

787720 

2-71 

897516 

i -63 

890204 

4-34 

109796 

5i 

9.787883 

2*71 

9-897418 

1 64 

9-890465 

4-34 

10-109535 

52 

788045 

2-71 

897320 

1 -64 

890725 

4*34 

109275 

53 

788208 

2-71 

897222 

1 -64 

890986 

4.34 

109014 

54 

788370 

2*70 

897123 

1 -64 

891247 

4.34 

108753 

55 

788532 

2-70 

897025 

1-64 

891507 

4*34 

108493 

56 

788694 

2-70 

896926 

1-64 

891768 

4*34 

108232 

5 ? 

7^8856 

2*70 

896828 

1 -64 

892028 

4.34 

10797-2 

56 

789018 

2-70 

896729 

1 -64 

892289 

4 • 34 

107711 

59 

789180 

2-70 

8966J( 

1-64 

892549 

4.34 

107451 

60 

789342 

2-69 

896532 

1 -64 

892810 

4.34 

107190 


Cosine | D. 

Sine 

D. 

Cotang. 

D. 

Tang. 


(52 DEGREES.) 


— NJ(OK5WION3NiW(OlO OJOJOJOJCOCOOJUiCOU) 

OJ^s 0-4 COsO O *■• K2 ^ O—J GOO o ~ to Co £n O-J GOO O *-« to Oo £n G7* O- 4 GOO O - M ^ O s ^J GOO O " W OJJi\ g< C'-J OCNO © 
















































66 (38 DEGREES.) A TABLE OF LOGARITHMIC 



Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


• 

0 

9*789342 

2-69 

9-896532 

1 -64 

9-892810 

4-34 

io-107190 

60 

1 

789504 

2-69 

896433 

1 -65 

893070 

4.34 

106980 


2 

789665 

2-69 

896335 

i .65 

8 9 333 1 

4-34 

106669 

58 

3 

789827 

2-69 

896236 

1 -65 

893591 

4-34 

106409 

57 

4 

789988 

2-69 

896137 

1 *65 

8 9 38 oi 

4 84 

106149 

56 

5 

790149 

2-69 

896038 

1 -65 

894111 

4 • 34 

106889 

55 

6 

790310 

2-68 

893989 

1 -65 

894371 

4 • 34 

106629 

34 

7 

790471 

2-68 

896840 

1 *65 

894662 

4-33 

io 5368 

53 

8 

790682 

2-68 

896741 

1 *65 

894892 

4-33 

106108 

52 

9 

790793 

2-68 

893641 

1 *65 

890162 

4-33 

104848 

5 i 

10 

790954 

2-68 

893542 

1 *65 

890412 

4-33 

104588 

5 o 

11 

9-791115 

2-68 

9-896443 

1-66 

9*896672 

4-33 

10 *104328 

49 

12 

791275 

2-67 

895343 

1*66 

890962 

4-33 

104068 

48 ; 

i 3 

791436 

2-67 

893244 

1*66 

896192 

4-33 

1o 38 o 8 

47 

i 4 

791696 

2-67 

893145 

1 *66 

896462 

4-33 

io 3548 

46 

i 5 

791737 

2-67 

896043 

1 *66 

896712 

4-33 

103288 

45 

16 

791917 

2-67 

894945 

1 *66 

896971 

4-33 

103029 

44 

n 

792077 

2-67 

894846 

1 *66 

897261 

4-33 

102769 

43 

18 

792237 

2-66 

894746 

1 *66 

897491 

4-33 

102609 

42 

19 

792397 

2-66 

894646 

1 *66 

897761 

4 • 33 

102249 

4i 

20 

792607 

2-66 

894646 

1 *66 

898010 

4-33 

101990 

40 

21 

9.792716 

2-66 

9•894446 

1-67 

9-898270 

4-33 

io-101730 

3 o 

22 

792876 

2-66 

894346 

1-67 

898560 

4-33 

101470 

38 

23 

79308 5 

2-66 

894246 

1.67 

898789 

4-33 

101211 

3- 

24 

793195 

2-65 

894146 

1-67 

899049 

4-32 

100961 

36 

25 

793334 

2-65 

894046 

1 *67 

899808 

4-32 

100692 

35 

26 

7935 i 4 

2-65 

893946 

1-67 

899668 

4-32 

100482 

34 

27 

793673 

2-65 

893846 

1 -67 

899827 

4-32 

100173 

33 

28 

793832 

2-65 

893745 

1-67 

900086 

4-32 

099914 

32 

29 

793991 

2-65 

893645 

1-67 

900346 

4-32 

099654 

3i 

3 o 

7941 5 o 

2-64 

893544 

1-67 

900605 

4-32 

099395 

3o 

3i 

9-794308 

2-64 

9-893 444 

1-68 

9-900864 

4-32 

10-099136 

20 

32 

794467 

2-64 

893343 

1 -68 

901124 

4-32 

098876 

28 

33 

794626 

2-64 

893243 

i-68 

901 383 

4-32 

098617 

27 

34 

794784 

2-64 

893142 

i-68 

901642 

4-32 

098358 

26 

35 

794942 

2-64 

893041 

i-68 

901901 

4-32 

098099 

25 

36 

796-01 

2-64 

892940 

1-68 

902160 

4-32 

097840 

24 

3 ? 

796269 

2-63 

892839 

i-68 

902419 

4-32 

097681 

23 

38 

796417 

2-63 

892739 

i-68 

902679 

4-32 

097321 

22 

39 

795575 

2-63 

892638 

1 -68 

902988 

4-32 

097062 

21 

40 

796733 

2-63 

892536 

1-68 

903197 

4 - 3 i 

096803 

20 

4 i 

9.793891 

2-63 

9-892435 

1 -69 

9-903455 

4 - 3 i 

10-096545 

>9 

42 

796049 

2-63 

892334 

1 -69 

903714 

4 - 3 i 

096286 

18 

43 

796206 

2-63 

892233 

1 -69 

903973 

4 * 3 i 

096027 

n 

44 

796364 

2-62 

892132 

1 -69 

904282 

4 - 3 i 

095768 

16 

45 

796521 

2-62 

892030 

1 -69 

904491 

4 - 3 i 

096609 

i 5 

46 

796679 

2-62 

891929 

1 -69 

904730 

4 - 3 i 

096260 

14 

47 

796836 

2-62 

891827 

1 -69 

905008 

4 • 3 1 

09499 2 

i 3 

48 

796903 

2-62 

891726 

1 -69 

905267 

4 - 3 i 

094783 

11 i 

49 

7971 5 c 

2-61 

891624 

1 -69 

905526 

4 - 3 i 

094474 

it 1 

5 o 

797307 

2-61 

891523 

1.70 

906784 

4 - 3 i 

094216 

1? • 

5 i 

9.797464 

2-6i 

9-891421 

1-70 

9•906043 

4 - 3 i 

10*093957 

9 

52 

797621 

2-6i 

891319 

1-70 

906302 

4 - 3 i 

093698 

8 

53 

797777 

2-61 

891217 

1-70 

906660 

4 - 3 i 

093440 

7 

54 

797934 

2-6l 

891116 

1 -70 

90681 Q 

4 • 3 i 

093181 

6 

55 

798091 

2-61 

891013 

1-70 

907077 

4 * 31 

092923 

5 

56 

; 798247 

2-61 

890911 

1-70 

907386 

4 * 3 1 

092664 

4 

57 

798403 

2-60 

890809 

1-70 

907694 

4 - 3 1 

092406 

3 

58 

798560 

2 -6o 

890707 

1 -70 

907802 

4 * 3 1 

092148 

2 

5 9 

798716 

2-60 

89060 5 

1 -70 

908 111 

4 - 3 o 

091889 

1 

6 >o 

798872 

2-60 

890608 

1-70 

908369 

4 - 3 o 

091631 

0 

! Cosine 

L - - 

D. 

Sine 

IX 

1 Cotang, 

D. 

Tiiug^ 

M. 

— - 


(51 DEGREES.) 




















































SINES AND TANGENTS. (39 DEGREES.; 57 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9*798872 

2-60 

9-890503 

1-70 

9-908369 

4 - 3 o 

10-091631 

60 

i 

799028 

2-60 

890400 

i- 7 * 

908628 

4 - 3 o 

091372 

5 9 

2 

799 184 

2 • 60 

890'? ?8 

i* 7 i 

908886 

4 - 3 o 

091114 

58 

3 

799339 

2-59 

8901 )5 

1-71 

9 ° 9 ! 44 

4 * 3 o 

090856 

57 

4 

799493 

2-59 

890093 

I- 7 1 

909402 

4 - 3 o 

090598 

56 

5 

799601 

2-59 

889990 

1 *7 1 

909660 

4 - 3 o 

090340 

55 

6 

799806 

2-69 

8808S8 

1-71 

909918 

4 • 3 o 

090082 

04 

7 

799962 

2-59 

889785 

1-71 

910177 

4 - 3 o 

089823 

53 

8 

800117 

2-59 

889682 

1-71 

910435 

4 - 3 o 

089565 

52 

9 

800272 

2-58 

889579 

1-71 

91o 6 o 3 

4 - 3 o 

089807 

5 i 

10 

800427 

2*58 

889477 

1 *7 1 

910931 

4 - 3 o 

089049 

5 o 

ii 

9*8oo582 

2 - 5 S 

9-889874 

1-72 

9-911209 

4 - 3 o 

10-088791 

49 

12 

800737 

2-58 

889271 

1-72 

911467 

4 - 3 o 

088533 

48 

i 3 

800892 

2 • 5 S 

889168 

I -72 

911724 

4 - 3 o 

088276 

47 

U 

801047 

2-58 

880064 

I -72 

911982 

4 * 3 o 

088018 

46 

1 *5 

801201 

2-58 

888961 

I -72 

912240 

4 - 3 o 

087760 

45 

16 

8 oi 356 

2 - 5 ~i 

888858 

1-72 

912498 

4 - 3 o 

087502 

44 

*7 

8 oi 5 i1 

2 - 5 ~l 

888755 

I -72 

912756 

4 - 3 o 

087244 

43 

i 8 

8 oi 665 

2-57 

88865 i 

I -72 

9i3oi4 

4-29 

086986 

42 

*9 

801819 

2 - 5 ~l 

888548 

1-72 

913271 

4-29 

086729 

4 ! 

*20 

801973 

2 - 5 i 

888444 

1-73 

913529 

4-29 

08647 1 

4 o 

21 

9*802128 

2 - 5 -] 

9- 88834 c 

1-73 

9-913787 

4-29 

io-o 862 i 3 

3 9 

22 

802282 

2-56 

888237 

1-73 

914044 

4-29 

085956 

38 

23 

802436 

2-56 

888 i 34 

1-73 

914302 

4-29 

085698 

37 

24 

802089 

2-56 

888 o 3 o 

1 -73 

914360 

4-29 

085440 

36 

25 

802743 

2-56 

887926 

1 - 7 3 

914817 

4-29 

o 85 i 83 

35 

26 

802897 

2-56 

887822 

i -73 

91507 5 

4-29 

084925 

34 

27 

8 o 3 « 3 o 

2-56 

887718 

i *73 

9 i 5332 

4-29 

084668 

33 

28 

8 o 32 o 4 

?*56 

887614 

1-73 

915590 

4*29 

084410 

32 

29 

8 o 3357 

2-55 

887610 

1-7 3 

915847 

4-29 

o84i53 

3 i 

3 o 

8 o 35 n 

2-55 

887406 

1-74 

916104 

4-29 

o 838 q 6 

3 o 

3 i 

9•803664 

2-55 

9-887302 

1-74 

9-916362 

4-29 

io-o 83638 

29 

32 

803817 

2-55 

887198 

1*74 

916619 

4-29 

o 8338 i 

28 

33 

803970 

2-55 

887093 

i -74 

916877 

4.29 

o 83 i 23 

27 

34 

804123 

2-55 

886989 

1-74 

917134 

4.29 

082866 

26 

35 

804276 

2-54 

886880 

1-74 

917391 

4*29 

082609 

25 

36 

804428 

2-54 

886780 

c -74 

917648 

4.29 

082352 

24 

3 7 

804381 

2-54 

886676 

1-74 

917906 

4-29 

082095 

23 

38 

804734 

2-54 

886571 

i -74 

9181 63 

4-28 

081837 

22 

39 

804886 

2-54 

886466 

1-74 

918420 

4-28 

o 8 i 58 o 

21 

4 o 

8 o 5 o 39 

2-54 

886362 

i - 7 5 

918677 

4-28 

o 8 i 323 

20 

4 i 

9-805191 

2-54 

Q- 886257 

1*75 

9 - 9 iB 934 

4-28 

10-081066 

*9 

42 

8 o 5343 

2-53 

886 1 62 

1-75 

919*9* 

4-28 

080809 

18 

43 

8 o 5493 

2-53 

886047 

i - 7 5 

919448 

4*28 

o 8 o 552 

*7 

44 

8 o 5647 

2-53 

883942 

1-76 

919705 

4*28 

080295 

16 

45 

805799 

2-53 

88583 7 

i - 7 5 

919962 

4-28 

o 8 oo 38 

i 5 

46 

805931 

2-53 

885732 

I - 7 3 

920219 

4-28 

079781 

14 

47 

8061o 3 

2-53 

885627 

i - 7 5 

920476 

4-28 

079524 

i 3 

48 

806254 

2-53 

885522 

i- 7 5 

920733 

4-28 

079267 

12 

49 

806406 

2-52 

8854 i 6 

i- 7 5 

920990 

4-28 

079010 

11 

1 5 c 

806337 

2-52 

8853 11 

1-76 

921247 

4-28 

078753 

to 

5 i 

9 806709 

2-52 

9 - 8852 o 5 

1-76 

9-92i5o3 

4-28 

10-078497 

9 

32 

806860 

2-52 

885 100 

1-76 

921760 

4-28 

078240 

8 

53 

8070! 1 

2-52 

884994 

1-76 

922017 

4-28 

077983 

n 

54 

807163 

2-52 

884889 

1-76 

922274 

4-28 

077726 

6 

55 

807314 

2-52 

884783 

1-76 

92253 o 

4-28 

077470 

5 

56 

807463 

2 • 51 

884677 

1-76 

922787 

4-28 

077213 

4 

57 

807616 

2 • 51 

884572 

1 -76 

923 o 44 

4-28 

076956 

3 

58 

807766 

2 • 5 l 

884466 

1-76 

9233 oo 

4-28 

. 076700 

a 

59 

807917 

2 ■ 51 

884360 

1-76 

923557 

4-27 

076443 

1 

60 

808067 

2 - 51 

884234 

1.77 

92381 3 

4-27 

076187 

0 


Coaine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(50 D 3GHKK6.) 
































































/ 


58 (40 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

■ 

Cotang. 


0 

9-878067 

2 • 5 1 

9-884264 

i-77 

9-923813 

4-27 

10-076187 

60 

i 

808218 

2 • 51 

884148 

i-77 

924070 

4-27 

076980 

59 

2 

8o8368 

2 - 51 

884042 

i-77 

924327 

4-27 

076673 

58 

3 

808519 

2-5 o 

883 9 36 

i-77 

924583 

4-27 

076417 

cl 

4 

808 (”>69 

2-5 o 

883829 

i-77 

924840 

4-27 

075160 

56 

5 

808819 

2-5 o 

883723 

1.77 

925096 

4-27 

074904 

55 

6 

808969 

2-5 o 

8836n 

i*77 

925302 

4-27 

074648 

54 

7 

809119 

2-5 o 

883510 

i-77 

920609 

4-27 

074391 

53 

8 

809269 

2-5 o 

8834o4 

i'll 

926865 

4-27 

074135 

52 

9 

809419 

2-49 

883297 

1 -78 

926122 

4-27 

073878 

|5i 

10 

809669 

2-49 

883191 

1-78 

926378 

4-27 

073622 

5o 

ii 

9-809718 

2-49 

9.883o84 

1 -78 

9•926634 

4-27 

io-073366 

49 

12 

809868 

2-49 

882077 

1 -78 

926890 

4-27 

073110 

48 

i3 

810017 

2-49 

882871 

1.78 

927147 

4-27 

072853 

47 

U 

810167 

2-49 

882764 

1 -78 

927403 

4-27 

072697 

46 

i 5 

8io3i6 

2-48 

882657 

1 -78 

927609 

4-27 

072341 

45 

16 

8)0465 

2-48 

88255o 

1 -78 

927915 

4-27 

072085 

44 

11 

8)0614 

2-48 

882443 

1-78 

928171 

4-27 

071829 

43 

i8 

810763 

2-48 

882336 

1-79 

928427 

4-27 

07 1 673 

42 

19 

810912 

2-48 

882229 

1-79 

928683 

4-27 

071317 

4i 

20 

811061 

2-48 

882121 

1 '79 

928940 

4-27 

071060 

40 

21 

9-811210 

2-48 

9-882014 

1-79 

9-929196 

4-27 

10-070804 

39 

22 

811 358 

2-47 

881907 

1-79 

929402 

4-27 

070548 

38 

23 

81 1 507 

2-47 

881799 

1.79 

9297 oS 

4-27 

070292 

37 

24 

81i655 

2-47 

88 1 692 

1.79 

929964 

4-26 

070086 

36 

25 

8 11 804 

2-47 

88 1 584 

1 *79 

980220 

4-26 

069780 

35 

26 

811952 

2-47 

881477 

1-79 

980475 

4-26 

069625 

34 

27 

812100 

2-47 

88 1 369 

1.79 

930731 

4-26 

069269 

33 

28 

812248 

2-47 

881261 

1 -8o 

930987 

4-26 

o6ooi3 

32 

29 

812396 

2-46 

881 1 53 

1 -8o 

931243 

4-26 

060757 

3i 

3o 

812544 

2-46 

881046 

1 -8o 

931499 

4-26 

0685oi 

3o 

3i 

9-812692 

2-46 

9-880933 

1 -8o 

9-931755 

4-26 

10-068245 

29 

32 

812840 

2-46 

88o83o 

1 -8o 

932010 

4-26 

067990 

28 

33 

812988 

2-46 

880722 

1 -8o 

982266 

4-26 

067734 

27 

34 

8i3i35 

2-46 

880613 

1 -8o 

932522 

4- 26 

067478 

26 

35 

8i3283 

2-46 

88o5o5 

1 -8o 

932778 

4-26 

067222 

25 

36 

8i343o 

2-45 

880397 

1 -8o 

933o33 

4-26 

066967 

24 

37 

813678 

2-45 

880289 

1 -81 

933289 

4-26 

066711 

23 

38 

813726 

2-45 

880180 

1 -81 

933540 

4-26 

0664^5 

22 

3 9 

813872 

2-45 

880072 

1 -8i 

9338oo 

4-26 

066200 

21 

40 

814019 

2-45 

879963 

1-81 

934 o 56 

4-26 

066944 

20 

4i 

9-814166 

2-46 

9-879855 

1 • 81 

9-934311 

4-26 

10-065689 

JO 

42 

814313 

2-45 

879746 

1 • 81 

934867 

4-26 

o 65433 

18 

43 

814460 

2-44 

879637 

1-81 

934823 

4-26 

065177 

17 

44 

814607 

2-44 

879629 

1 81 

935078 

4-26 

064922 

l6 

45 

814753 

2-44 

879420 

1-81 

935333 

4-26 

064667 

i5 

46 

814900 

a-44 

879311 

1 -8i 

935589 

4-26 

064411 

14 

47 

815o46 

2-44 

879202 

1 -82 

980844 

4-26 

064106 

i3 

48 

815193 

2-44 

879098 

1 -82 

936100 

4*26 

063900 

12 

49 

8 i 5339 

2-44 

878984 

1 -82 

936355 

4-36 

o 63645 

1 

5o 

8i 5485 

2-43 

878875 

1 -82 

936610 

4-26 

063390 

.0 

5i 

9-8 i 563 i 

2-43 

9-878766 

1-82 

9 • 986866 

4-25 

1 0 • o63 1 34 

0 

52 

816778 

2-43 

878656 

1 -82 

937121 

4-25 

062879 

8 

53 

816924 

2-43 

878547 

1-82 

987376 

4-25 

062624 

7 

54 

816069 

2-43 

878438 

1-82 

937632 

4-25 

062368 

6 

55 

816210 

2-43 

873328 

1 -82 

937887 

4-25 

062 11 3 

5 

5t 

8i636i 

2-43 

8782 1 9 

1-83 

938142 

4-25 

061858 

4 

5 1 

8 i 65 o 7 

2-42 

878109 

1-83 

93S398 

4-25 

061602 

3 

58 

816652 

2-42 

877999 

i-83 

9 386 o 3 

4-25 

061347 

2 

59 

816798 

2-42 

877800 

i-83 

938908 

4-20 

061092 

1 

60 

816943 

2-42 

877780 

i-83 

939 1 63 

4-25 

060837 

1 0 

1 

L.. 

Cosine 

D. 

Sine 

D. 

Cotang. 

r. 

Tang. 

i M. 


(49 DEGREES.) 




















































SINES AND TANGENTS. (41 DEGREES.) 


59 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-816943 

2-42 

9.877780 

i -83 

9-939163 

4-25 

10-060837 

60 

i 

817088 

2-42 

877670 

1-83 

939418 

4-25 

060682 

69 

2 

817233 

2-42 

877060 

i -83 

939673 

4-25 

060327 

58 

3 

8*7879 

2-42 

877460 

1 -83 

939928 

4-26 

060072 

57 

4 

817524 

2-41 

877340 

i -83 

940183 

4-26 

059817 

56 

5 

817668 

2 - 4 i 

877230 

1 -84 

940438 

4-25 

069662 

55 

6 

817813 

2-41 

877120 

1-84 

940694 

4-25 

o 5 g 3 o 6 

54 

7 

817968 

1 • 4 1 

877010 

1-84 

940949 

4-25 

o 5 oo 5 i 

53 

fe 

8 i 8 io 3 

2 - 4 i 

876899 

1-84 

941204 

4-25 

008796 

52 

9 

816247 

2-41 

806789 

1-84 

94*458 

4-25 

058542 

5 i 

10 

8 i 83 9 2 

2-41 

876678 

1-84 

941714 

4-25 

058286 

5 o 

ii 

1 9.81 8536 

2-40 

9-876568 

1-84 

9-941968 

4-25 

io-o 58 o 32 

49 

12 

818681 

2-40 

876467 

1 -84 

942223 

4 25 

007777 

48 

i 3 

818826 

2-40 

876347 

1-84 

942478 

4-25 

057522 

47 

14 

818969 

2 -40 

876236 

1 -85 

9427)3 

4-20 

007267 

46 

i 5 

819113 

2-40 

876125 

i-8o 

942988 

4-25 

057012 

45 

16 

819267 

2-40 

876014 

1 -85 

943243 

4-25 

006767 

44 

17 

819401 

2-40 

875904 

1-85 

943498 

4-25 

o 565 o 2 

43 

18 

819545 

2-39 

875793 

1 -85 

943762 

4-25 

066248 

42 

19 

819689 

2 - 3 g 

875682 

1 -So 

944007 

4-25 

060993 

4 i 

20 

819832 

2-39 

875571 

1 -85 

944262 

4-25 

0557 38 

4 o 

21 

9-819976 

2-39 

9-876469 

1 *85 

9 - 9445 i 7 

4-25 

io-o 55483 

3 9 

22 

820120 

2-39 

875348 

1 -85 

944771 

4-24 

055229 

38 

23 

820263 

2-39 

876237 

1 -85 

90026 

4-24 

054974 

37 

24 

820406 

2-39 

876126 

1 -86 

946281 

4-24 

054719 

36 

25 

82o55o 

2-38 

876014 

1 -86 

945535 

4-24 

054460 

35 

26 

820693 

2-38 

874903 

1 -86 

946790 

4-24 

054210 

34 

2 Z 

820836 

2-38 

874791 

i-86 

946045 

4-24 

053955 

33 

28 

820979 

2-38 

874680 

i-86 

946299 

4-24 

053701 

32 

29 

821122 

2-38 

874568 

i-86 

946554 

4-24 

053446 

3 i 

3 o 

821265 

2-38 

874466 

1-86 

946808 

4-24 

053192 

3 o 

3 i 

Q-821407 

2-38 

9-874344 

i-86 

9-947063 

4-24 

10-052937 

29 

32 

82i55o 

2-38 

874232 

1-87 

947318 

4-24 

052682 

28 

33 

821693 

2-37 

874121 

1.87 

947572 

4-24 

062428 

27 

34 

82 i 835 

2-37 

874009 

1.87 

947826 

4-24 

062174 

26 

35 

821977 

2.37 

873896 

1.87 

948081 

4-24 

051919 

25 

36 

822120 

2-37 

873784 

1-87 

948336 

4-24 

051664 

24 

37 

822262 

2.37 

873672 

1-87 

948090 

4-24 

o 5 i 4 io 

23 

38 

822404 

2-37 

873660 

1-87 

948844 

4-24 

0011 56 

22 

3 9 

822646 

2-37 

873448 

1-87 

949099 

4-24 

000901 

21 

40 

822688 

2-36 

873335 

1-87 

949353 

4-24 

060647 

20 

4 i 

9-822830 

2-36 

9-873223 

1-87 

9-949607 

4-24 

10-000393 

*9 

42 

822972 

2-36 

873110 

i-88 

949862 

4-24 

o 5 oi 38 

18 

43 

823114 

2-36 

872998 

i-88 

960116 

4-24 

049884 

17 

44 

823255 

2-36 

872885 

i-88 

960670 

4-24 

04 g 63 o 

16 

45 

823397 

2-36 

872772 

i-88 

960626 

4-24 

049376 

i 5 

46 

823539 

2-36 

872669 

1-88 

960879 

4-24 

049121 

14 

47 

828680 

2-35 

872647 

1-88 

95 ii 33 

4-24 

048867 

i 3 

48 

823821 

2-35 

872434 

1-88 

90 i 388 

4-24 

048612 

12 

49 

823963 

2-35 

872321 

i-88 

961642 

4-24 

. 048358 

11 

5 t? 

824104 

2-35 

872208 

i-88 

961896 

4-24 

/ 048104 

10 

5 i 

9-824246 

2-35 

9-872095 

1-89 

9-962150 

4-24 

10-047800 

9 

52 

824886 

2-35 

871981 

1 -89 

962406 

4-24 

047696 

8 

53 

824527 

2-35 

871868 

1 -89 

962659 

4-24 

047341 

7 

54 

824668 

2-34 

871755 

1 -89 

962913 

4 - 24 

047087 

6 

5 c 

824808 

2-34 

871641 

1 -89 

963167 

4-23 

046833 

5 

5 1 

824949 

2-34 

871628 

1-89 

963421 

4-23 

046679 

4 

57 

820090 

2-34 

871414 

1 -89 

963675 

4-23 

046320 


58 

82023c 

2-34 

871301 

1-89 

963929 

4-23 

046071 

2 

59 

825371 

2-34 

871187 

1 -89 

964186 

4-23 

0458 17 

j 

60 

82551I 

2-34 

87107) 

1 -90 

964437 

4-26 

045563 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(48 DEGREES.) 




















































60 


(42 DEGREES.} A TABLE OF LOGARITHMIC 


* 


M. 

Sine 

1 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

r 

9• 8255 11 

2*34 

9*871073 

1 *90 

9*954437 

4*23 

10*045500 

60 

i 

82565 i 

2*33 

870960 

1 *90 

954691 

4-23 

045309 

1 5 9 1 

2 

826791 

2*33 

870846 

1 *90 

954946 

4*23 

o 45 o 5 d 

1 58 

3 

826931 

2*33 

870732 

1 *90 

955200 

4*23 

044800 

57 

4 

826071 

2*33 

870618 

1*90 

966454 

4*23 

044646 

56 l 

5 

826211 

2*33 

870504 

1 *90 

955707 

4*23 

044293 

55 

6 

82635 i 

2*33 

870390 

1 *90 

955961 

4*23 

044039 

54 

7 

826491 

2*33 

870276 

1 *90 

9562 i 5 

4*23 

043785 

53 

8 

82663 i 

2*33 

870161 

1 *90 

966469 

4*23 

o 4353 i 

52 

9 

826770 

2*32 

870047 

1 *91 

966728 

4*23 

043277 

5 i 

IC 

826910 

2*32 

869933 

1*91 

956977 

4-23 

o 43 o 23 

5 o 

11 

9*827049 

2*32 

9*869818 

1 *91 

9.957231 

4*23 

10*042769 

4 q 

il 

827189 

2*32 

869704 

1.91 

9^7485 

4*23 

0425 1 5 

48 

i 3 

827328 

2*32 

869689 

1.91 

957739 

4*23 

042261 

47 

U 

827467 

2*32 

869474 

1.91 

967993 

4*23 

042007 

46 

i 5 

827606 

2*32 

869860 

1 *91 

968246 

4*23 

041764 

45 

16 

827746 

2*32 

869245 

1 *91 

9585 oo 

4*23 

o 4 i 5 oo 

44 

n 

827884 

2 - 31 

869130 

1*91 

968754 

4*23 

041246 

43 

18 

828023 

2 • 3 I 

869016 

1*92 

959008 

4*23 

040992 

42 

x 9 

828162 

2 • 31 

868900 

1 *92 

959262 

4*23 

040738 

4 i 

20 

8283oi 

2 • 31 

868785 

1*92 

969516 

4*23 

040484 

4 o 

21 

9*828439 

2 • 31 

9*868670 

1 *92 

9*969769 

4*23 

io*o 4 o 23 i 

3 o 

22 

828678 

2 • 31 

868555 

1 *92 

960023 

4*23 

039977 

38 

23 

828716 

2 * 31 

868440 

1*92 

960277 

4*23 

039723 

37 

24 

828855 

2 * 3 o 

868324 

1 *92 

960531 

4*23 

039469 

36 

25 

828993 

2 * 3 o 

868209 

1 *92 

960784 

4*23 

o 3 g 2 i 6 

35 

26 

829131 

2 * 3 o 

868093 

1*92 

961038 

4*23 

038962 

34 

27 

829269 

2 * 3 o 

867978 

1 *93 

961291 

4*23 

038709 

33 

28 

829407 

2 * 3 o 

867862 

1 *93 

961645 

4*23 

038455 

32 

29 

829545 

2 * 3 o 

867747 

1 *93 

961799 

4*23 

o 3 S 2 oi 

3 i 

3 o 

829683 

2 * 3 o 

867631 

1 *93 

962062 

4*23 

037948 

3 o 

3 i 

9*829821 

2*29 

9•86761 5 

1*93 

9*962306 

4*23 

10*037694 

29 

32 

829959 

2*29 

867399 

1 *93 

962560 

4*23 

037440 

28 

33 

830097 

2*29 

867283 

1 *98 

962813 

4*23 

037187 

27 

34 

830234 

2 • 29 

867167 

1 *93 

963067 

4*23 

o 36933 

26 

35 

83 o 372 

2*29 

867061 

1 *93 

963320 

4*23 

o 3668 o 

25 

36 

83 o 5 o 9 

2*29 

866935 

1*94 

963674 

4*23 

036426 

24 

37 

830646 

2*29 

866819 

1*94 

963827 

4*23 

o 36 i 73 

23 

38 

830784 

2*29 

866700 

1 *94 

964081 

4*23 

035919 

22 

39 

830921 

2*28 

866586 

1 *94 

964335 

4*23 

o 35665 

21 

4 o 

83 io 58 

2*28 

866470 

1 *94 

964588 

4*22 

o 354 i 2 

20 

41 

9*83i196 

2*28 

9*866353 

1*94 

9*964842 

4*22 

io*o 35 i 58 

IO 

42 

83 i 332 

2*28 

866237 

1*94 

966095 

4*22 

034906 

l8 

43 

83 1469 

2*28 

866120 

1*94 

965349 

4*22 

o 3465 i 

17 

44 

83 1606 

2*28 

866004 

1 *96 

966602 

4*22 

034398 

16 

45 

831742 

2*28 

865887 

1 *95 

965855 

4*22 

034145 

i 5 

46 

83 1879 

2*28 

866770 

1 *95 

966105 

4*22 

033891 

14 

47 

8320!5 

2*27 

865653 

1 *95 

966362 

4*22 

o 33638 

i 3 

48 

832 1 52 

2*27 

865536 

1 *96 

966616 

4*22 

033384 

12 

49 

832288 

2*27 

865419 

1 *95 

966869 

4*22 

o 3 3 1 3 1 

11 

5 o 

832425 

2*27 

8653 o 2 

1 *95 

967123 

4*22 

032877 

10 

5 i 

q- 83256 i 

2*27 

9 *865 1 85 

1 *95 

9*967376 

4*22 

10*032624 

9—1 

52 

832697 

2*27 

866068 

1 *96 

967629 

4*22 

032371 

8 

53 

832833 

2*27 

864960 

1 *96 

967883 

4*22 

0321 17 

7 

54 

832969 

2*26 

864833 

1 *96 

968136 

4*22 

o 3 1 864 

6 

55 

833 1 03 

2*26 

8647 1 6 

1 *96 

968389 

4*22 

o 3 i 6 i 1 

5 

56 

833241 

2*26 

864698 

1 *96 

968643 

4*22 

o 3 i 357 

4 

5 7 

833377 

2*26 

864481 

1 *96 

968896 

4*22 

o 3 i104 

3 

58 

8335 12 

2*26 

864363 

1 *96 

969149 

4*22 

o 3 o 85 i 

a 

5 9 

833648 

2*26 

864245 : 

1 *96 

969403 

4*22 

o 3 o 597 

1 

60 | 

833783 

2*26 

864127 

1 *96 

969666 

4*22 

o 3 o 344 

0 

j Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. i 

M. 


(47 DEGREES.) 































































SINES AND TANGENTS. (43 DEGREES.) 63 


r- - 

M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9 833783 

2-26 

9-864127 

1 -96 

9-969666 

4-22 

io-o 3 o 344 

60 

i 

833919 

2-25 

864010 

1 -96 

969909 

4-22 

030091 

5 9 

a 

834 o 54 

2-25 

863892 

1-91 

970162 

4'22 

029838 

58 

3 

834189 

2-25 

863774 

1-97 

970416 

4-22 

029684 

67 

4 

1 834320 

2-25 

863656 

1.97 

970669 

4-22 

029331 

56 

5 

i 83446 o 

2-25 

863538 

1-97 

970922 

4-22 

029078 

55 

6 

1 834595 

2-25 

863419 

1-97 

971175 

4-22 

028825 

54 

7 

1 83473 o 

2-25 

8633 oi 

1.97 

971429 

4-22 

028671 

53 

8 

; 834865 

2-25 

863 1 83 

1-97 

971682 

4-22 

028318 

52 

9 

, 834999 

2 24 

863 o 64 

1-97 

971935 

4-22 

028065 

5 i 

10 

835 1 34 . 

O . 9 < 

- 2.|. 

862946 

1 -98 

972188 

4-22 

027812 

5 o 

11 

9-835269 

2-24 

9-862827 

1 -98 

9-972441 

4-22 

10-027559 

49 

12 

8354 o 3 

2-24 

862709 

1 -98 

972694 

4-22 

027306 

48 

i 3 

835538 

2-24 

862690 

1 -98 

972948 

4-22 

027062 

47 

i 4 

835672 

2-24 

862471 

1 -98 

973201 

4-22 

026799 

46 

i 5 

835807 

2-24 

862353 

1 -98 

973454 

4-22 

026646 

45 

16 

835941 

2-24 

862234 

1 -98 

973707 

4-22 

020293 

44 

! 7 

836075 

2-23 

86211 5 

1 -98 

976960 

4-22 

026040 

43 

18 

836209 

2-23 

861996 

1 -98 

974213 

4-22 

026787 

42 

19 

836343 

2-23 

861877 

1-98 

974466 

4-22 

025534 

4 i 

20 

836477 

2-23 

861 7 58 

1.99 

974719 

4-22 

025281 

4 o 

21 

9- 8366 11 

2-23 

9 - 86 i 638 

1-99 

9-974973 

4-22 

10-025027 

3 9 

22 

886745 

2-23 

861 5 19 

1 -99 

975226 

4-22 

024^74 

33 

23 

836878 

2-23 

861400 

1*99 

976479 

4-22 

024521 

37 

24 

837012 

2-22 

861280 

1 -99 

976732 

4-22 

024268 

36 

25 

837146 

2-22 

861161 

1 -99 

976985 

4-22 

024015 

35 

26 

837279 

2-22 

861041 

1-99 

976238 

4-22 

023762 

34 

27 

837412 

2-22 

860922 

1 ’99 

976491 

4-22 

123509 

33 

28 

837546 

2-22 

860802 

1 ’99 

976744 

4-22 

023256 

32 

l 9 

837679 

2-22 

860682 

2-00 

976997 

4-22 

o 23 oo 3 

3 i 

3 o 

837812 

2-22 

860662 

2-00 

977200 

4-22 

022760 

3 o 

3 i 

9-837945 

2-22 

9 - 860442 

2-00 

9-977603 

4-22 

10-022497 

29 

32 

838078 

2-21 

860322 

2-00 

977756 

4-22 

022244 

28 

33 

838211 

2-21 

860202 

2-00 

978009 

4-22 

021991 

27 

34 

838344 

2-21 

860082 

2-00 

978262 

4-22 

021738 

26 

35 

838477 

2-21 

859062 

2-00 

97851 5 

4-22 

021485 

25 

35 

8386 10 

2-21 

859842 

2-00 

978768 

4-22 

021232 

24 

37 

888742 

2-21 

869721 

2-01 

979021 

4-22 

020979 

23 

38 

838875 

2-21 

859601 

2-01 

979274 

4-22 

020726 

22 

39 

839007 

2-21 

869480 

2-01 

979627 

4-22 

020473 

21 

40 

839140 

2-20 

869360 

2-01 

979780 

4-22 

020220 

20 

41 

9-839272 

2-20 

9-859239 

2-01 

9-980033 

4-22 

10-019967 

19 

42 

839404 

2-20 

869119 

2-01 

980286 

4-22 

019714 

l8 

43 

83 9 536 

2-20 

868998 

2-01 

980538 

4-22 

OI9462 

17 

44 

839668 

2-20 

868877 

2-01 

980791 

4.21 

OI9209 

l6 

45 

839800 

2-20 

868756 

2-02 

981044 

4-21 

018966 

ID 

46 

839932 

2-20 

858635 

2-02 

981297 

4-21 

018703 

14 

47 

840064 

2-19 

8585 14 

2-02 

981650 

4-21 

0I8450 

i 3 

48 

840196 

2-19 

8583 9 3 

2-02 

981 8 o 3 

4-21 

01819*7 

12 

49 

840328 

2-19 

858272 

2-02 

982056 

4-21 

017944 

11 

5 o 

840459 

2-19 

858 i 5 i 

2-02 

982309 

4-21 

017691 

*9 

5 i 

9-840591 

2-19 

9-858029 

2-02 

9-982562 

4-21 

io-oi 7438 

9 

52 

840722 

2-19 

857908 

2-02 

982814 

4-21 

017186 

8 

53 

840854 

2-19 

867786 

2-02 

983067 

4-21 

016933 

T 

54 

840985 

2-19 

857665 

2-03 

983320 

4-21 

016680 

6 

55 

841116 

2- l8 

867543 

2 -o 3 

983573 

4-21 

016427 

5 

5i 

841247 

2-18 

867422 

2 -o 3 

983826 

4-21 

016174 

4 

5" i 

841378 

2-18 

8573 oo 

2 -o 3 

984079 

4»2I 

015921 

3 

5 i* > 

84 5 og 

2 • 18 

857178 

2 -o 3 

9843)1 

4-21 

016669 

2 

59 ! 

841640 

2- l8 

867066 

2 • o 3 

984684 

4-21 

016416 

1 

60 | 

841771 

2 • l8 

866934 

2 -o 3 1 

984837 

4-21 

01 5 1 63 

0 


Cosine 

D. 

Sine i 

D. 

Cotang. 

D. 

Tang. 

M. 


(46 DEGREES.) 
























































62 


(44 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-84177* 

2 

18 

9-866934 

2 -o 3 

9-984837 

4-21 

io-oi 5 i 63 

1 60 

i 

841902 

2 

18 

8568 12 

2 • o 3 

986090 

4-21 

0I49I0 

5 o 

2 

842033 

2 

18 

866690 

2 -o 4 

985343 

4-21 

014657 

58 

3 

842163 

2 

*7 

856568 

2-04 

985596 

4-21 

014404 

57 

4 

842294 

2 

'7 

856446 

2 -04 

986848 

4-21 

014152 

56 

5 

842424 

2 

>7 

856323 

2-04 

986131 

4-21 

013899 

55 

6 

842555 

2 

*7 

8502 oi 

2 -04 

986334 

4-21 

013646 

54 

7 

842685 

2 

*7 

856078 

2 -04 

986607 

4-21 

oi 33 9 3 

53 

8 

842815 

2 

*7 

855906 

2 ■ 04 

986860 

4-21 

01 3 140 

52 

9 

842946 

2 

17 

855833 

2-04 

987112 

4-21 

012888 

5 i 

IO 

843076 

2 

*7 

855711 

2 • o 5 

987365 

4-21 

012635 

5 o 

11 

9-843206 

2 

16 

9-855588 

2 -o 5 

9-987618 

4-21 

10-012382 

49 

12 

843336 

2 

16 

855405 

2 -o 5 

987871 

4-21 

012129 

48 

i 3 

843466 

2 

16 

855342 

2 • o 5 

988123 

4-21 

011877 

47 

14 

843^5 

2 

16 

855219 

2 -o 5 

988376 

4-21 

011624 

46 

i 5 

843725 

2 

16 

855096 

2 -o 5 

988629 

4-21 

011371 

45 

16 

843855 

2 

16 

854973 

2 • o 5 

988882 

4-21 

011118 

44 

>7 

843984 

2 

16 

85485 o 

2 -o 5 

989134 

4-21 

010866 

43 

18 

844 114 

2 

i 5 

854727 

2-06 

989387 

4-21 

01061 3 

42 

19 

844243 

2 

i 5 

8546 o 3 

2-06 

989640 

4-21 

oio 36 o 

41 

20 

844372 

2 

i 5 

854480 

2-06 

989893 

4-21 

010107 

4 o 

21 

9-844302 

2 

1 5 

9-854356 

2 • 06 

9-990145 

4-21 

10-009855 

3 9 

22 

84463 1 

2 

i 5 

854233 

2-06 

990398 

4-21 

009602 

38 

23 

844760 

2 

i 5 

854109 

2 • 06 

990651 

4-21 

009349 

37 

24 

844889 

2 

i 5 

853986 

2 • 06 

990903 

4-21 

009097 

36 

25 

843018 

2 

i 5 

853862 

2-06 

9911 56 

4-21 

008844 

35 

26 

843147 

2 

i 5 

853738 

2 • 06 

99*409 

4-21 

008591 

34 

27 

846276 

2 

14 

8536 i 4 

2-07 

991662 

4-21 

oo 8338 

33 

23 

8454 o 5 

2 

U 

853490 

2-07 

991914 

4-21 

008086 

32 

’9 

845533 

2 

14 

853366 

2-07 

992167 

4-21 

007833 

3 i 

3 o 

843662 

2 

14 

853242 

2-07 

992420 

4-21 

007580 

3 o 

3 i 

9-845790 

2 

14 

9 - 853 118 

2-07 

9-992672 

4-21 

10-007328 

29 

32 

845919 

2 

*4 

852994 

2-07 

992925 

4-21 

007075 

28 

33 

846047 

2 

14 

852869 

2-07 

993178 

4-21 

006822 

27 

34 

846176 

2 

14 

852748 

2-07 

9 9 343 o 

4-21 

006670 

26 

35 

846304 

2 

14 

852620 

2-07 

9 9 3683 

4-21 

oo 63 17 

25 

36 

846432 

2 

i 3 

862496 

2-08 

993 9 36 

4-21 

006064 

24 

3 7 

84656 o 

2 

i 3 

852371 

2- 08 

994189 

4-21 

oo 58 i1 

23 

38 

846688 

2 

i 3 

852247 

2-08 

994441 

4-21 

oo 555 o 

22 

3 9 

846816 

2 

i 3 

852122 

2-08 

994694 

4-21 

oo 53 o 6 

21 

4 o 

846944 

2 

i 3 

851997 

2 • 08 

994947 

4-21 

oo 5 o 53 

20 

4 i 

9.847071 

2 

i 3 

9-851872 

2-08 

9-995199 

4-21 

10-004801 

I 9 

42 

847199 

2 

i 3 

851747 

2-08 

995462 

4-21 

004648 

l8 

43 

847327 

2 

i 3 

85 i 622 

2-08 

995705 

4-21 

004295 

*7 

44 

847454 

2 

12 

85 1497 

2-09 

995957 

4-21 

004043 

16 

45 

847582 

2 

12 

85 13-72 

2-09 

996210 

4-21 

003790 

i 5 

46 

8477°9 

2 

12 

85 1246 

2-09 

996463 

4-21 

oo 3537 

14 

47 

847836 

2 

12 

85 1121 

2-09 

99671 5 

4-21 

008285 

i 3 

43 

847964 

2 

12 

850996 

2-09 

996968 

4-21 

oo3o32 

12 

49 

848091 

2 

12 

850870 

2-0 9 

997221 

4-21 

002779 

11 

5 o 

848218 

2 

12 

850745 

2-09 

997473 

4-21 

002027 

10 

5 i 

9-848345 

2 

12 

9 - 85 o 6 i 9 

2-09 

9.997726 

4-21 

10-002,274 

9 

52 

848472 

2 

11 

860493 

2-10 

997979 

4-21 

002021 

8 

53 

848599 

2 

11 

85 o 368 

2-10 

998231 

4-21 

001769 

7 

51 

848726 

2 

11 

850242 

2- 10 

998484 

4-21 

001 5 1 6 

6 

55 

848852 

2 

11 

85 oi16 

2 • 1 C 

998737 

4-21 

001263 

5 

56 

848979 

2 

11 

849990 

2-10 

998989 

4-21 

001011 

4 

57 

849106 

2 

11 

849864 

2- 10 

999242 

4-21 

000758 

3 

58 

849232 

2 

11 

849738 

2- 10 

999495 

4-21 

ooooo 5 

2 

59 

84935 (J 

2 

11 

849611 

2-10 

999748 

4-21 

000253 

1 

60 

849480 

2 

11 

849485 

2 • 10 

10•000000 

4-21 

10•000000 

0 


Cosine 

I). 

Sine 

i). 

Cotang. 

D. 

Tung. 

M. 


(45 DECREES.) 











































A TABLE OF NATURAL SINES, 


63 



0 Deg. 

1 Deg. 

2 Deg. 

3 Deg. 

4 Deg. 


M 

S. 

C. S. 

IS. 

C. S. 

S. 

0 . S. 

S. 

C. S. 

S. 

C. S. 

M 

0 

00000 

Unit. 

01745 

99985 

03490 

99939 

o 5234 

99863 

06976 

QQl 56 

60 

i 

00029 

1*0000 

01774 

99984 

o 35 i 9 

999 38 

o 5263 

99861 

07006 

99754 

69 

2 

ooo 58 

I-0000 

oi 8 o 3 

99984 

o 3548 

99937 

05292 

99860 

07034 

99762 

58 

3 

00087 

1•0000 

oi 832 

99983 

03577 

99936 

o 532 1 

99868 

07063 

99760 

5 7 

4 

00116 

I*0000 

01862 

99983 

o 36 o 6 

99935 

o 535 o 

99867 

07092 

99748 

56 

5 

00145 

[1*0000 

01891 

99982 

o 3635 

99934 

05379 

99855 

07121 

99746 

55 

6 

00170 I*0000 

01920 

99982 

o 3664 

99933 

o 54 o 8 

99854 

07160 

99744 

54 

7 

00204 

I *0000. 

01949 

99981 

03693 

99932 

05437 

99852 

07179 

99742 

53 j 

8 

00233 

1*0000 

01978 

99980 

03723 

99931 

o 5466 

99851 

07208 

99740 

52 J 

9 

00262 

1*0000 

02007 

99980 

03752 

99930 

06495 

99849 

07237 

99738 

5 i 

IO 

00291 

I .0000 

02036 

99979 

03781 

99929 

o 5524 

99847 

07266 

99736 

5 o 

11 

00320 

99999 

02065 

99979 

o 38 io 

99927 

o 5553 

99846 

07295 

99734 

49 

12 

00349 

99999 

02094 

99978 

03839 

99926 

o 5582 

99844 

07324 

99731 

48 

i 3 

00378 

99999 

02123 

99977 

o 3868 

99926 

o 56 i 1 

99842 

07353 

99729 

47 

14 

00407 

99999 

02 1 52 

99977 

03897 

99924 

o 564 o 

99841 

07382 

99727 

46 

i 5 

00436 

99999 

02181 

99976 

03926 

99923 

o 566 q 

99839 

07411 

99726 

45 

16 

00465 

99999 

02211 

99976 

o 3 g 55 

99922 

05698 

99838 

07440 

99723 

44 

17 

00495 

99999 

02240 

99975 

03984 

99921 

05727 

99836 

07469 

99721 

43 

18 

oo 524 

99999 

02269 

99974 

0401 3 

99910 

05766 

99834 

07498 

99719 

42 

19 

oo 553 

99998 

02298 

99974 

04042 

99918 

05785 

99833 

07527 

99716 

4 i 

20 

oo 582 

99998 

02327 

99973 

04071 

99917 

o 58 i 4 

99831 

07556 

99714 

40 

21 

00611 

99998 

02356 

99972 

04100 

99916 

o 5844 

99829 

07685 

99712 

3 9 

22 

00640 

99998 

02385 

99972 

04129 

999 15 

05873 

99827 

07614 

99710 

38 

23 

00669 

99998 

02414 

99971 

° 4 i 5 o 

99913 

06902 

99826 

07643 

99708 

37 

24 

00698 

99998 

02443 

99970 

04188 

99912 

05931 

99824 

07672 

99705 

36 

25 

00727 

99997 

02472 

99969 

04217 

99911 

05960 

99822 

07701 

99703 

35 

26 

00756 

99997 

02501 

99969 

04246 

99910 

05980 

99821 

07730 

99701 

34 

27 

00785 

99997 

o 253 o 

99968 

04275 

99909 

06018 

99819 

07760 

99699 

33 

28 

00814 

99997 

0256 o 

99967 

o 43 o 4 

99907 

06047 

99817 

07788 

qq6q6 

32 

29 

00844 

99996 

02589 

99966 

04333 

90906 

06076 

99815 

07817 

99694 

3 i 

3 o 

00873 

99996 

02618 

99966 

04362 

99905 

o 6 io 5 

99813 

07846 

99692 

3 o 

3 i 

00902 

99996 

02647 

99965 

04391 

99904 

061 34 

99812 

07875 

99689 

29 

32 

009J1 

99996 

02676 

99964 

04420 

90 QO 2 

061 63 

99810) 

07904 

99687 

?H 

33 

00960 

99995 

02705 

99963 

o 444 q 

999OI 

06192 

99808 

07933 

99685 

27 

34 

00989 

99995 

02734 

99963 

04478 

999OO 

06221 

99806 

07962 

99683 

26 

35 

01018 

9999 5 

02763 

99962 

04507 

99898 

o 6 p 5 o 

99804 

07991 

99680 

25 

36 

01047 

99995 

02792 

999 6 ' 

04536 

99897 

06279 

99803 

08020 

99678 

24 

37 

01076 

99994 

02821 

99960 

04565 

qq8q6 

o 63 o 8 

99801 

08049 

99676 

23 

38 

01 io 5 

99994 

o 285 o 

99959 

04594 

99894 

o 6337 

99799 

08078 

99673 

22 

39 

01134 

99994 

02879, 

99959 

04623 

qo 8 o 3 

o 6366 

99797 

08107 

99671 

21 

40 

01164 

99993 

02 QOO 

99958 

04653 

99892 

06395 

99795 

081 36 

99668 

20 

41 

01193 

90993 

02938 

999^7 

04682 

99890 

06424 

99793 

081 65 

99666 

J 9 

42 

01222 

99993 

02967 

99956 

04711 

99880 

o 6453 

99792 

08194 

99664 

18 

43 

01201 

99992 

O2996 

9 qq 55 

o474o 

99888 

06482 

99700 

08223 

99661 

17 

44 

01280 

99992 

o 3 o 25 

99954 

04760 

99886 

o 65 i 1 

99788 

08262 

99659 

16 

45 

01309 

99991 

o 3 o 54 

99953 

04798 

99885 

o 654 o 

99786 

08281 

99657 

ID 

46 

oi 338 

99991 

o 3 o 83 

99952 

04827 

99883 

06669 

99784 

o 83 io 

99664 

14 

47 

01367 

99991 

o 3 i 12 

99952 

04856 

99882 

06598 

99782 

08339 

99652 

i 3 

48 

01396 

99990 

o 3 i 4 i 

9995 i 

04885 

99881 

06627 

99780 

o 8368 

99649 

12 

49 

01426 

99990 

03170 

99950 

04914 

99879 

o 6656 

99778 

08397 

99647 

11 

5 o 

01454 

99989 

03199 

99949 

04943 

99878 

o 6685 

99776 

08426 

99644 

10 

5 i 

oi 483 

99989 

03228 

99948 

04972 

99876 

06714 

99774 

08455 

99642 

9 

52 

01 5 1 3 

99980 

03257 

99947 

o 5 ooi 

99875 

06743 

99772 

08484 

99639 

8 

53 

01542 

99988 

o 3286 

99946 

o 5 o 3 o 

99873 

06773 

99770 

o 85 i 3 

99637 

7 

54 

0071 

qqq88 

o 33 i 6 

99945 

o 5 o 59 

99872 

06802 

99768 

08542 

99635 

6 

55 

01600 

99987 

o 3345 

99944 

o 5 o 88 

99870 

o 683 1 

99766 

08671 

99632 

5 

56 

01629 

99987 

o 3374 

99943 

o 5 117 

00860 

06860 

99764 

08600 

99630 

4 

57 

01 658 

99986 

o 34 o 3 

99942 

o 5 i 46 

99867 

06889 

99762 

08629 

99627 

*3 

u 

58 

01687 

99986 

o 3432 

99941 

o5i-]5 

99866 

06918 

99760 

o 8658 

99626 

2 

59 

01716 

99985 

03461 

99940 

o 52 o 5 

99864 

06947 

99708 

08687 

99622 

I 

M 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

M 


89 Deg. 

88 Deg. 

87 Deg. 

86 Deg. 

85 Deg. 












































































64 


A TABLE OF NATURAL SINES, 



5 Deg. 

6 Deg. 

7 Deg. 

8 Deg. 

9 Deg. 


M 

S. 

I C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S 

S. 

C S. 

M 

o 

08716 

99619 

10453 

99452 

12187 

99265 

18917 

99027 

16643 

98769 

60 

i 

08745 90017 

10482 

99449 

12216 

99261 

13946 

99026 

15672 

98764 

69 

2 

08774 

99614 

loJi 1 

99446 

12245 

99248 

13975 

99019 

15701 

98760 

58 

3 

o88o3 

99612 

j 1o 54 o 

99443 

12274 

99 2 44 

14004 

99016 

1573o 

98755 

57 

4 

o883i 

99609 

10669 

99440 

12302 

99240 

i 4 o 33 

99011 

15768 

98761 

56 

5 

08860 

99607 

10597 

99437 

12331 

99237 

14061 

99006 

16787 

98746 

55 

6 

08889 

99604 

10626 

99434 

12360 

99233 

14090 

99002 

15816 

98741 

54 

7 

08918 

qq6o2 

io655 

99431 

12380 

99230 

14119 

98998 

16845 

98737 

53 

8 

08947 

99599 

10684 

99428 

12418 

99226 

14148 

98994 

15873 

98732 

52 

9 

08976 

99596 

10713 

99424 

12447 

99222 

14177 

98990 

15902 

98728 

5i 

IO 

09006 

99694 

10742 

99421 

12476 

99219 

14205 

98986 

15931 

98723 

5o 

11 

09034 

99691 

10771 

99418 

I25 o 4 

99216 

14234 

9898 2 

*6969 

98718 

49 

12 

09063 

99588 

10800 

99415 

12533 

99211 

14263 

98978 

15988 

98714 

48 

i3 

,.09092 

99586 

10829 

99412 

12662 

99208 

14292 

98973 

16017 

98709 

47 

i4 

09121 

99583 

io858 

99409 

12591 

99204 

14320 

98969 

16046 

98704 

46 

i5 

09150 

99580 

10887 

99406 

12620 

99200 

14349 

98960 

16074 

98700 

45 

16 

09179 

99578 

10916 

99402 

12649 

99197 

14378 

98961 

i6io3 

98695 

44 

17 

09208 

99675 

10945 

99399 

12678 

99103 

14407 

9 8 9 5 7 

1613 2 

98690 

43 

18 

09237 

99572 

10973 

99396 

12706 

99189 

14436 

98963 

16160 

98686 

42 

19 

09266 

99670 

11002 

99393 

12735 

99186 

14464 

98948 

16189 

98681 

41 

20 

09295 

99667 

11 o31 

99390 

12764 

99182 

14493 

98944 

16218 

98676 

4o 

21 

09324 

99664 

11060 

99386 

12793 

99178 

14522 

98940 

16246 

98671 

3 9 

22 

09353 

99562 

11080 

99383 

12822 

99175 

i 455 i 

98936 

16275 

98667 

38 

23 

09382 

99559 

11118 

99380 

12861 

99>7i 

14580 

98931 

i 63 o 4 

98662 

37 

24 

09411 

99556 

11147 

99377 

12880 

99 i6 7 

14608 

98927 

i 6333 

98657 

36 

25 

09440 

99553 

11176 

99374! 

12908 

99163 

14637 

98926 

16361 

98662 

35 

26 

09469 

9955 i 

11 2 o 5 

99370 

12937 

99160 

14666 

98919 

16390 

98648 

34 

27 

09498 

99548 

11234 

99367 

12966 

99166 

14695 

98914 

16419 

98643 

33 

28 

09627 

99545 

11263 

99364 

12995 

99152 

14723 

98910 

16447 

98638 

32 

29 

09556 

99542 

11291 

99360 

i 3 o 24 

99148 

14752 

98906 

16476 

98633 

3i 

3o 

o 9 585 

99540 

11320 

99307 

i 3 o 53 

99144 

14781 

98902 

i65o5 

98629 

3o 

31 

09614 

99537 

11349 

99354 

i 3 o 8 i 

99141 

14810 

98897 

16533 

98624 

29 

32 

09642 

99534 

11378 

9935 i 

13110 

99137 

14838 

98896 

16562 

98619 

28 

33 

09671 

9953 i 

11407 

99347 

1313o 

99i33 

14867 

98889 

16591 

98614 

27 

34 

09700 

99628 

11436 

99344 

i 3 i 68 

99129 

14896 

9S884 

16620 

98609 

26 

35 

09729 

99526 

11465 

99341 

1 3 i 97 

99125 

14925 

98880 

16648 

98604 

25 

36 

09753 

99523 

11494 

99337 

13226 

99122 

14954 

98876 

16677 

98600 

24 

37 

09787 

99520 

11523 

99334 

13264 

99118 

14982 

98871 

16706 

98595 

23 

33 

09816 

99 5 1 7 

11552 

9933 i 

13283 

991*4 

16011 

98867 

16734 

98590 

22 

3 9 

09845 

99514 

1 i58o 

99327 

13312 

99110 

i 5 o 4 o 

9 8863 

16763 

9 8585 

21 

40 

09874 

99511 

11609 

99324 

i 334 i 

99106 

15069 

9 8858 

16792 

98580 

20 

4i 

09903 

99508 

11638 

99320 

13370 

99102 

15097 

98854 

16820 

98575 

IO 

42 

09932 

99506 

11667 

99317 

13399 

99098 

15126 

98849 

16849 

98570 

l8 

43 

09961 

995o3 

11696 

99314 

13427 

99094 

15155 

98845 

16878 

98565 

17 

44 

09990 

99500 

11725 

99310 

13456 

99001 

15184 

98841 

16906 

98561 

IO 

45 

10019 

99497 

11764 

99307 

13485 

99087 

16212 

9 8836 

16935 

98556 

i5 

46 

10048 

99494 

11783 

993 o3 

i35i4 

99083 

15241 

98832 

16964 

9855 i 

14 

47 

10077 

99491 

11812 

99300 

13543 

99079 

16270 

98827 

16992 

98546 

j3 

48 

10106 

99488 

11840 

99297 

13572 

9907 D 

15292 

98826 

17021 

986411 

12 

i 9 

ioi 35 

99486 

11869 

99293 

i36oo 

99071 

15327 

98818 

17060 

98536 

11 

5o 

10164 

99482 

11898 

99290 

13629 

99067 

15356 

98814 

17078 

9853 1 

10 

5i 

10192 

99479 

11927 

99286 

13658 

99063 

15385 

98809 

17107 

98626 

9 

52 

10221 

99476 

11956 

99283 

13687 

99059 

15414 

98803 

17136 

98521 

3 

53 

10250 

99473 

11985 

99279 

13716 

99055 

16442 

98800 

17164 

98516 

7 

54 

10279 

99470 

12014 

99276 

13744 

9905 1 

15471 

98796 

171931 

98311 

6 

55 

io3o8 

99467 

12043 

99272 

13773 

99°47 

i55oo 

98791 

17222! 

98606 

5 

56 

io 337 

99464 

12071 

99269 

i 38 o 2 

99043 

i 5529 

98787 

I 725 o 

98501 

4 

J7 

io366 

99461 

12100 

99260 

13 331 

9 Qo 39 

10007 

98782 

17270 

98496 

3 

58 

10395 

99458 

1 2120 

99262 

13 860 

99035 

15586 

98778 

17308 

98491 

2 

59 

10424 

99455 

12158 

99268 

13889 

99031 

156i 5 

98773 

17336 

98486 

1 

M 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

M 


84 Deg. 

83 Deg. 

82 Deg. 

81 Deg : 

80 Deg 































































































A TABLE OF NATURAL SINES. 


66 



10 Deg. 

11 Deg. 

12 Deg. 

13 Deg. 

14 Deg. 

M 

S. 

C. S. 

S. 

0. S. 

S. 

0. S. 

S. 

C. S. 

S. 

C. S. 

0 

17365 

98481 

19081 

98163 

20791 

97815 

22496 

97437 

24192 

97 o 3 o 

i 

17393 

98476 

19109 

98157 

20820 

97809 

22523 

9743o 

24220 

9702.3 

2 

17422 

98471 

19138 

98152 

20848 

9780.31 

22552 

9742 4 

24249 

97 oi 5: 

3 

I745 i 

98466 

19167 

98146 

20877 

97797 

22580 

97417 

24277 

97008 

4 

17479 

98461 

19196 

98140 

20906 

9779 1 

2 26o8 

97411 

243 o 5' 

97001 

5 

17508 

98455 

19224 

98135 

20933 

977&4 

22637 

97404 

24333 

96994 

6 

17537 

98450 

19252 

98129 

20962 

97778 

22665 

97 3 9 8 

24362 

96987 

7 

17565 

98445 

19281 

98124 

20990 

97772 

22693 

97 3 9 i 

24390 

96980 

8 

17094 

98440 

19309 

98118 

21019 

97766 

22722 

97384 

24418 

96973 

9 

17623 

98435 

19338 

98112 

21047 

97760 

22750 

97378 

24446 

96966 

10 

17651 

98430 

19366 

98107 

21076 

97754 

22778 

97371 

24474 

96959 

11 

17680 

98425 

19396 

98101 

21104 

97748 

22807 

97365 

245o3 

96952 

12 

17708 

98420 

19423 

98096 

21132 

97742 

22835 

97358 

2453 i 

96945 

i3 

17737 

98414 

19452 

98090 

21161 

97735 

22863 

9735 i 

24559 

96937 

i4 

17766 

98400 

19481 

98084 

21189 

97729 

22892 

97345 

24587 

96930 

i5 

17794 

98404 

19609 

98079 

21218 

97723 

22920 

97338 

24616 

96923 

16 

17823 

983 qq 

19538 

98073 

21246 

97717 

22948 

9733 i 

24644 

96916 

i7 

17852 

98394 

19666 

98067 

21275 

97711 

22977 

97325 

24672 

96909 

18 

17880 

9838g 

19595 

98061 

2i3o3 

97705 

23 oo 5 

973 i 8 

24700 

96902 

19 

17909 

98383 

19623 

98056 

21331 

97698 

23 o 33 

973 ii 

24728 

96894 

20 

17937 

98378 

19652 

98o5o 

2i36o 

97692 

23062 

973 o 4 

24756 

96887 

21 

17966 

98373 

19680 

98044 

21388 

97686 

23090 

97298 

24784 

96880 

22 

17995 

98368 

I 97°9 

98039 

21417 

97680 

23118 

972m 

24813 

96873 

23 

18023 

98362 

19737 

98033 

21446 

97673 

23146 

97 2 84 

24841 

96866 

24 

i 8 o 52 

98357 

19766 

98027 

21474 

97667 

23176 

97278 

24869 

9 6858 

25 

18081 

98352 

19794 

98021 

21 5 o 2 

97661 

23203 

97271 

24897 

g685i 

26 

18109 

98347 

19823 

98016 

2 i 53 o 

97655 

23231 

97264 

24926 

96844 

27 

18138 

98841 

19861 

98010 

2155g 

97648 

23260 

97257 

24953 

96837 

28 

18166 

98336 

19880 

98004 

21587 

97642 

23288 

97251 

24982 

96829 

29 

18195 

9833 i 

19908 

97998 

21616 

97636 

23316 

97244 

26010 

96822 

3o 

18224 

98325 

19937 

97992 

21644 

97630 

23345 

97237 

25 o 38 

96815 

3i 

18252 

98320 

19965 

97987 

21672 

97623 

233 7 3 

97230 

25 o 66 

96807 

32 

18281 

98315 

x 9994 

97981 

21701 

97617 

23401 

97223 

2 5og4 

9680c 

33 

18809 

98310 

20022 

97975 

21729 

97611 

23429 

97217 

20122 

9679.3 

34 

18338 

983o4 

2 oo 5 i 

97969 

21758 

97604 

23458 

97210 

25151 

96786 

35 

18367 

98299 

20070 

979 63 

21786 

97598 

23486 

97208 

25179 

96778 

36 

i 83 9 5 

98294 

20108 

97958 

21814 

97592 

235i4 

97106 

26207 

96771 

37 

18424 

98288 

2 oi 36 

97 9 52 

21843 

97585 

23542 

97189 

25236 

96764 

38 

18452 

98283 

2 oi 65 

9794b 

21871 

97579 

23571 

97182 

25263 

96756 

39 

18481 

98277 

20193 

97940 

21899 

97578 

28699 

97176 

2.6291 

0749 

3o 

i85og 

98272 

20222 

97934 

21928 

97566 

23627 

97'69 

25320 

96742 

41 

i8538 

98267 

20250 

97928 

21956 

9756o 

23656 

97162 

25348 

96734 

42 

18567 

98261 

20279 

97922 

21985 

97553 

23684 

97i55 

26376 

96727 

43 

18695 

98256 

20307 

97916 

220l3 

97547 

23712 

97148 

25404 

96719 

44 

18624 

98250 

2 o 336 

97910 

22041 

97541 

23740 

97141 

25432 

9671? 

45 

i 8652 

98245 

2 o 364 

97 9 °5 

22070 

97534 

23769 

97134 

25460 

96700 

46 

18681 

98240 

20393 

97899 

22098 

97528 

23797 

97127 

25488 

96697 

47 

18710 

98234 

20421 

97893 

22126 

97521 

2.3825 

97120 

25616 

96690 

48 

18738 

98229 

2 o 45 o 

97887 

22155 

97515 

23853 

97113 

25545 

96682 

49 

18767 

98223 

20478 

97881 

22183 

975o8 

2'3882 

97106 

25573 

96675 

5o 

18795 

98218 

20507 

97875 

22212 

97502 

23gio 

97100 

256 oi 

96667 

5i 

18824 

98212 

2 o 536 

97869 

22240 

974o6 

23938 

97093 

25629 

96660 

52 

18862 

98207 

2 o 563 

97866 

22268 

97489 

23966 

97086 

25657 

96604 

53 

18881 

98201 

2o5g2 

97857 

22297 

97483 

23996 

97079 

25685 

96645 

54 

18910 

98196 

20620 

97851 

22326 

97476 

24023 

97072 

257i3 

96688 

55 

18938 

98190 

20649 

97845 

22353 

97470 

24 o 5 i 

97065 

26741 

96680 

56 

18967 

9 8 i 85 

20677 

97839 

22382 

97463 

24079 

97058 

25769 

96628 

57 

18995 

98 1 79 

20706 

97833 

22410 

97457 

24108 

97061 

25798 

96615 

58 

19024 

98174 

20734 

97827 

22438 

9745o 

24136 

97044 

25826 

96608 

5 9 

19052 

98168 

20763 

97821 

22467 

97444 

24164 

97037 

25854 

96600 

M 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 


79 Deg. 

78 Deg. 

77 Deg. 

76 Deg. 

75 Deg. 1 


_i HaHWxiuk'MHIOUIOMMIO CoUWCUOJOJWOJUiOJ^^s^^A 
Ui 0~J OOO o *“ M WJ>> CJ> (T'-J GCvO o — UiO'-J QC'C O — w G»Jj^ UiO 1 ^ COO O — >o GJ-O. <J* C--~J CCAO O -> u <J ■ 0^~-J Gf. O O 














































































66 


A TABLE OF NATURAL SINES. 



15 Deg. 

16 Deg. 

17 Deg. 

18 Deg. 

19 Deg. 


M 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

1 S. C. 

M 

n 

25882 

96693 

27564 

96126 

29237 

9563 o 

30902 

96106 

32557 

94552 

60 

i 

25910 

96585 

27692 

96118 

29265 

96622 

30929 

95097 

32584 

94542 

59 

2 

2D938 

96678 

27620 

961101 

29293 

96618 

30957 

96088 

32612 

94633 

58 

3 

25966 

96670 

27648 

96102 

29321 

956 o 5 

30985 

96079 

82689 

94523 

57 

4 

20994 

96662 

27676 

96094 

29348 

96696 

31012 

90070 

32667 

945 i 4 

56 

5 

26022 

96555 

27704 

960861 

29376 

q 5588 

31040 

96061 

32694 

945 o 4 

55 

6 

26o5o 

96647 

27731 

96078 

29404 

q 557 q 

3 1068 

95 o 52 

32722 

94493 

54 

/ 

26079 

96540 

27759 

96070 

29432 

Q 55 7 i 

3 lOg 5 

95 o 43 

32749 

94480 

53 

8 

26107 

96532 

27787 

96062 

29460 

95562 

3 ii 23 

95 o 33 

32777 

94475 

52 

9 

26 i 35 

96524 

27815 

96064! 

29487 

95554 

3 11 5 1 

95024 

32804 

94466 

5 i 

10 

26163 

96517 

27843 

96046 

2951 5 

95545 

31178 

96015 

32832 

94457 

5 o 

11 

26191 

96D09 

27871 

96087 

29543 

95536 

3 1206 

96006 

32869 

94447 

49 

12 

26219 

96602 

27899 

96029, 

2 9 5 7 i 

q 5528 

3 i 233 

94997 

32887 

94438 

48 

i 3 

26247 

96494 

27927 

96021 

29599 

95519 

31261 

94988 

32914 

94428 

47 

14 

26275 

96466 

27955 

96013 

29626 

955 i 1 

31289 

94979 

32942 

9 44 i 8 

46 

i 5 

263o3 

96479 

27983 

96006 

29654 

955 o 2 

3 i 3 i 6 

94970 

32969 

94409 

45 

16 

2633 1 

96471 

28011 

9 5 997 

29682 

95493 

3 1344 

94961 

32997 

94399 

44 

17 

26359 

96463 

28039 

95989 

29710 

96485 

31372 

94952 

33o24 

q 4390 

43 

18 

26387 

96406 

28067 

95981 

29737 

96476 

31899 

94943 

33 o 5 i 

q 438 o 

42 

19 

26416 

96448 

28095 

9 5 9 72 

29765 

95467 

31427 

94933 

33079 

94370 

4i 

20 

26443 

96440 

28123 

9 5 9 64 

29793 

95459 

3 i 454 

94924 

33 106 

q 436 i 

40 

21 

26471 

96463 

28 i 5 o 

95956 

29821 

95460 

3 i 482 

94916 

33 1 34 

9435 i 

3 9 

22 

26600 

96425 

28178 

95948 

29849 

95441 

3 i 5 io 

94906 

33 161 

94342 

38 

23 

26528 

96417 

28206 

95940 

29876 

95433 

3 1 537 

94807 

33189 

94332 

37 

24 

26556 

96410 

28234 

q 5 q 3 i 

29904 

95424 

3 1 565 

94888 

332 i 6 

94322 

36 

25 

26584 

96402 

28262 

9 5 g 23 

29932 

954 i 5 

3 1593 

94878 

33244 

q 43 1 3 

35 

26 

26612 

96394 

28290 

9591 5 

29960 

95407 

31620 

94869 

33271 

q43o3 

34 

27 

26640 

96386 

283 i 8 

95907 

29987 

95398 

31648 

94860 

33298 

94293 

33 

28 

26668 

96379 

28346 

95898 

3 ooi 5 

95389 

31675 

9485 i 

33326 

94284 

3a 

29 

26696 

96371 

28374 

95890 

30043 

9538 o| 

3 1703 

94842 

33353 

94274 

3 i 

3 o 

26724 

96363 

28402 

9 5882 

30071 

95372 

3 i 73 o 

94832 

3338 i 

94264 

3o 

3 i 

26752 

9 6355 

28429 

95874 

3 ooq 8 

95363 

3 i 758 

94823 

334 o 8 

94254 

29 

32 

26780 

96347 

28457 

q 5865 

30126 

95354 

3 i 7 86 

94814 

33436 

94245 

28 

33 

26808 

96340 

28485 

95857 

3 oi 54 

95345 

3 181 3 

94805 

33463 

94235 

27 

34 

26836 

96332 

285 1 3 

95849 

30182 

95337 

3 i 84 i 

94795 

33490 

94225 

26 

35 

26864 

96324 

28541 

q 584 1 

30209 

95328 

3 1868 

94786 

335 i 8 

9421 5 

25 

36 

26892 

96316 

28569 

95832 

30237 

95319 

81896 

94777 

33545 

94206 

24 

37 

26920 

96308 

28597 

95824 

30265 

953 io 

31923 

94768 

33573 

9419 6 

23 

38 

26948 

96301 

28625 

9 58 i 6 

30292 

953 oi 

3 ig 5 1 

94758 

336 oo 

94186 

22 

3 9 

26976 

96293 

28652 

95807 

3 o 32 o 

95203 

31979 

94749 

33627 

94176 

21 

4 o 

27004 

96285 

28680 

95799 

3 o 348 

95284 

32 oo 6 

94740 

33655 

94167 

20 

4 i 

27032 

96277 

28708 

9 5 79 < 

30376 

96275 

32034 

9473 o 

33682 

94 i 57 

19 

42 

27060 

96269 

28736 

95782 

3 o 4 o 3 

96266 

32 o 6 i 

94721 

33710 

94147 

l8 

43 

27088 

96261 

28764 

95774 

3 o 43 1 

95257 

82089 

94712 

33737 

94187 

17 

44 

27116 

96253 

28792 

95766 

30459 

95248 

32 ii 6 

94702 

33764 

94127 

l6 

43 

27144 

96246 

28820 

95737 

3 o 486 

96240 

32144 

94693 

33792 

94118 

i5 

46 

27172 

9&238 

28847 

95749 

3 o 5 i 4 

9523 1 

32171 

94684 

33819 

94108 

14 

47 

27200 

96230 

28875 

95740 

3 o 542 

95222 

32199 

94674 

33846 

94098 

i 3 

48 

27228 

96222 

28903 

95732 

30570 

952 i 3 

32227 

94665 

33874 

94088 

12 

49 

27256 

96214 

28931 

95724 

80697 

96204 

32254 

94656 

33901 

94078 

11 

5c 

27284 

96206 

28959 

9 5 7 i5 

30625 

95196 

32282 

94646 

33929 

94068 

10 

5 i 

27312 

96198 

28987 

95707 

3 o 653 

95 i 86 

32309 

94637 

33956 

94068 

9 

52 

27340 

96 1 90 

29015 

95698 

3 o 68 o 

95 1 77 

32337 

94627 

33 9 83 

94049 


53 

27368 

96182 

29042 

95690 

30708 

96168 

32364 

94618 

34 oi 1 

94039 

7 

54 

27396 

96174 

29070 

96681 

30736 

9D159 

32392 

94609 

34038 

94029 

6 

3 D 

27424 

96166 

29098 

96673 

30763 

95 i 5 o 

32419 

94599 

3 406 5 

94019 

5 

56 

27462 

96158 

29126 

95664 

30791 

95142 

32447 

94590 

34093 

94009 

4 

57 

27480 

96100 

29154 

95656 

30819 

95 i 33 

32474 

94580 

34120 

9 3 999 

3 

58 

27508 

96142 

29182 

95647 

30846 

95124 

32502 

94571 

34 i 47 

q 3 q 8 q 

2 

5 9 

27536 

96134 

29209 

95639 

308741 9511 5 

32529 

9456 i 

34 n 5 

93979 

1 

M 

C. S. 1 s. 

C. S. 

S. 

C. S. 

s. 

C. S. 

S. 

C. S. 

S. 

M 


74 Deg. 

73 Deg. 

72 Deg. 

71 Deg. 

70 Deg. 

J 














































































A TABLE OF NATURAL SINES. 


67 


M 


9 

1C 

?i 

12 

1 3 

1 4 

1 5 

16 
i 

i 

19 

20 
21 
22 

23 

24 
20 
26 

27 

28 

29 

3 0 

3 1 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

5 0 

5 1 

52 

53 

54 

55 

56 

57 

58 

69 

M' 


20 Deg. 


s. c. s. 


34202 
34229 
3425t 
34284 
3 4311 
34339 
3*366 
343g3 
3442i 
34448 
34475 
345o3 
3453 o 
34557 
34584 
34612 

34639 

34666 

34694 

34721 

34748 

34775 

348o3 

3483o 

34857 

34884 

34912 

34939 

34966 

34993 

35o2i 

35o 48 
35o75 
35 io2 
35i3o 
35157 
35i 83 
352 ii 
35239 
35266 
35293 
35320 
35347 
35375 
35402 
35429 

35456 
35484 
3551 1 
35538 
35565 
35592 
35619 
35647 
30674 
35701 
35728 
35 7 55 
35782 
358 io 


C. S. 


93969 

93959 

93949 

93939 

93929 

Q3919 

98909 

93899 

93889 

9 38 79 
93869 
9 385 9 
93849 
93839 
93829 
9 3819 

93809 

9 3 779 

9 3 7&9 

9 3 7^9 

93748 

93738 

93728 

93718 

93708 

93698 

9 3688 

9 36 77 

93667 

93657 

93647 

93637 

93626 

93616 

93606 

93596 

93585 

93575 

93565 

9 3555 

98544 

93534 

93524 

935 i 4 

935 o 3 

93493 

93483 

9 3 472 

93462 

93462 

93441 

9343 i 

93420 

93410 

93400 

93389 

9 33 79 

93368 


S. 


69 Deg. 


21 Deg. 


s. 0. s. 


35837 

35864 

35891 

35918 

36945 

35973 

36ooo 

36027 

36064 

36o8i 

36io8 

36i35 

36162 

36190 

36217 

36244 

36271 

36298 

36325 

36352 

36379 

364o6 

36434 

36461 

36488 

365i5 

36542 

36569 

36596 

36623 

3665o 

36677 
36704 
36 7 3i 
36 7 58 
36785 
36812 
36839 
36867 

36894 

36921 

36948 

36975 

37002 

37029 

37056 

37083 

37110 

3 7 i3 7 

37164 

37191 

37218 

37245 

37272 

37299 

37326 

37353 

37380 

37407 

37434 


C. S. 


93358 

93348 

93337 

93327 

933 i 6 

933 o 6 

93295 

93285 

93274 

93264 

93253 

93243 

93232 

93222 

93211 

93201 

93190 
93180 
93169 
931 5 o 
93148 
93137 
93127 
93116 
93106 
93095 
93084 
93074 
93 o 63 
93 o 52 
93042 

93 o 3 i 

93020 

93010 

92999 

92988 

92978 

92967 

92956 

92945 

92935 

92924 

92913 

92902 

92892 

92881 

92870 

92859 

92849 

92838 

92827 

92816 

92805 

92794 

92784 

9 2 77 3 

92762 

92761 

92740 

92729 


S. 


68 Deg. 


22 Deg. 


S. 


37461 
37488 
375 i 5 
376421 
37069 
37696 
37022 j 
37649' 
37676 
37703 
37730 

3 7757 
37784 
37811 
3 7 838 
37865 

37892 

3 79*9 

37946 

3 797 3 

37999 

38026 

38 o 53 
38o8o 
38107 
38 1 34 
38 1 6 1 
38 1 88 
38215 
38241 
38268 

38295 

38322 

38349 

38376 

38403 

3843o 

38456 

38483 

385io 

38537 

38564 

385 9 i 

38617 

38644 

38671 

38698 

38725 

38752 

38778 

388o5 

38832 

3885 9 

38886 

38912 

38939 

38966 

38993 

39020 

39046 


C. S. 


c. s. 

92718 
92707 
92697 
92686 
9'. 675 
92 64 
92063 
92642 
92631 
92620 
92609 
92598 
92587 
92676 
92066 

92554 

92543 

92532 

92521 

92510 

92499 

92488 

9 2 477 

92466 

92455 

92444 

92432 

92421 

92410 

92390 

92388 

92377 

92366 

92355 

92343 

92332 

92321 

92310 

92299 

92207 

92276 

92265 

92254 

92243 

92231 

92220 

92209 

92198 

92186 

92175 

92164 

92 l 52 

92141 
92130 
92119 
92107 
92096 
92086j 
92073 
92062 


S. 


67 Deg. 


23 Deer. 


S. 


39073 

39100 

3 9 i2 7 

39153 

39180 

39207 

39234 

39260 

39287 

39314 

39341 

39367 

3939 
39421 

39448 

39474 

3 g 5 oi 

3 9 528 

39555 

39681 

39608 

39635 

3 g 66 i 

3 g 688 

39715 

39741 

39768 

39795 

3 q 822 

39848 

39875 

39902 

39928 

39955 

3998 

40008 
4 oo 35 
40062 
40088 
4oi 1 5 
4 oi 4 i 
40168 
40196 
40221 
40248 
40275 

4o3oi 
4 o 328 
4o355 
4o38i 
40408 
4 o 434 
40461 
40488 
4o5i4 
4o54 i 
40567 
40594 
40621 

40647 


C. S. 


92o3c 


C. S. 


y.y 

9I89I 


9 l833 

91822 

9l8l 

9*79 

91787 

9*775 

91764 

91762 

91741 

91729 

91718 

91706 

91694 
9 i683 
91671 
91660 
91648 
9 1636 
91625 
91613 
91601 
91690 
91578 
91566 
9 i 555 
9 i 543 
91 53 1 

91619 

9i5o8 

91496 

91484 

91472 

91461 

91449 

91437 

91426 

91414 

91402 

91890 

91378 

91366 


S. 


66 Deer. 


24 Deg. 


S. 

C. S. 

M 

40674 

9 i 355 

60 

> 40700 

9 i 343 

5 q 

M 40727 

91 33 1 

58 

>| 40753 

91319 

57 

40780 

91307 

56 

40806 

91295 

55 j 

4 o 833 

91283 

54 

40860 

91272 

53 

40886 

91260 

i $2 

4091 3 

91248 

5 i 

,40939 

91236 

5 o 

40966 

qi 224 

49 

40992 

91 2 I 2 

48 

41019 

91200 

47 

41045 

91188 

46 j 

41072 

91176 

45 

41098 

91164 

441 

41126 

91 I 52 

43 

411 5 1 

91140 

42 

41178 

91128 

41 

41204 

91116 

4 o 

41 23 1 

91104 

3 9 

41257 

41284 

91092 

91000 

38 

3 7 

4i3io 

91068 

36 

4i337 

9 io 56 

35 

41363 

91044 

34 

41890 

9 io 3'2 

33 

41416 

91020 

32 

4 1 443 

91008 

3 i 

41469 

90996 

3 o 

41496 

90984 

8 

41622 

90972 

41649 

90960 

27 

41670 

90948 

26 

41602 

90986 

90924 

25 ! 

41628 

24 ! 

41 655 

90911 

2<3 1 

41681 

90399 

90887 

22 j 

41707 

21 I 

4 H 3 4 

90876 

20 | 

41760 

90863 

19 | 

41787 

90861 

l8j 

4181 3 

90839 

17 j 

41840 

90826 

16 

41866 

90814 

i 51 

41892 

90802 

14 

41919 

41940 

90790 

i 3 

90773 

12 

41972 

90766 

11 

41998 

90753 

10 

42024 

90741 

9 

42o5i 

90729 

8 

42077 

90717 

7 

42104 

90704 

6 | 

42i3o 

90692 

5 

421 56 

90680 

4 i 

42183 

90668 

3 

42209 

90655 

2 | 

42230 

90643 

1 

C. S. 

S. 

M 

65 Dec 1 . 

- 


19 


































































































68 


A TABLE OF NATURAL SINES. 


M 

25 Deg. 

26 Deg. 

27 Deg. 

28 Deg. 

29 Deg. 

M 

60 

S 5 ? 

57 

56 

55 

54 

53 

53 

5i 

5o 

49 

48 

47 

46 

45 

44 

43 

42 

4i 

40 

3 9 

38 

1-, 
w / 

36 

35 

34 

33 

32 

3i 

3o 

20 
28 
27 
26 
25 

24 

23 

22 

21 

20 

10 
l8 

17 

l6 

i5 

14 

i3 

L 2 

11 

: 0 

J 

7 

6 

5 

4 

3 

3 

1 

M 

— 

S. 

C. S. 

8. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

JO 

11 

12 

13 

14 

15 

16 

n 

18 

20 

21 

22 

23 

24 

25 

26 

27 

28 
29 

l 3o 
i 3i 
! 32 
! 33 

34 

35 
! 36 

I 3 7 

1 38 

1 3o 
! 40 

41 

42 

43 

44 
46 

46 

47 

48 

49 

DO 

51 

52 

53 
04 

55 

56 

57 
53 
69 

42262 
42288 
42315 
4234 i 
42367 
42394 
42420 
42446 
42473 

42499 

42525 

42552 

42578 

42604 

4263 i 

42657 

42683 

42709 

42736 

42762 

42788 

42815 

42841 

42867 

42894 

42920 

42946 

42972 

42999 

43 o 25 

43 o 5 i 

43077 
43104 
43 i 3 o 
43 i 56 
43 i 82 
43200 
43235 
43261 
43287 
43313‘ 
4334o 
43366 
43392 
434 i 8 
43445 

43471 
43497 
43523 
4354c 
43570 
436o2 
43628 
43654 
4368o 
43706 
43 7 33 
43769 
43-780 
438 i 1 

90631 

90618 

90606 

90604 

90582 

90569 

90557 

90645 

90532 

90520 

90507 

90496 

90483 

90470 

90458 

90446 

90433 

90421 

90408 

90396 

9 o 383 

90371 

9o358 

90346 

90334 

90321 

90309 

90296 

90284 

90271 

90269 

90246 

90233 

90221 

90208 

90196 

90183 

90171 
90158 
90146 
90i33 
90120 
90108 
90095 
90082 
90070 

90057 

90045 

90032 

90019 

00007 

89904 

89981 

89968 

89956 

89943 

89930 

8(7918 

89905 
89892 

4383 7 

43863 

43889 

43916 

43942 

43968 

43994 

44020 

44046 

44072 

44098 

44124 

44 i 5 i 

44177 

44203 

44229 

44255 
44281 
44307 
44333 
44359 
44385 
444i 1 
44437 
44464 
44490 
445 i 6 
44542 
44568 
44594 
44620 

44646 

44672 

44698 

447 2 4 

447 5 o 

4477 6 

44802 

44828 

44854 

44880 

44906 

44932 

44958 

44984 

45 oio 

45 o 36 

45 o 62 

45 o 88 

45114 

45140 
45166 

46192 

46218 

45243 

46269 

46290 

45321 

45347 

45373 

89879 

89867 

89854 

89841 

89828 

89816 

89803 

89790 

89777 

89764 

89752 

89739 

89726 

89713 

89700 

89687 

89674 
89662 
89649 
8 9 636 
89623 
89610 

89607 

89584 

89571 

89558 

89545 

89532 

89519 

89506 

89493 

89480 

89467 

89454 

89441 

89428 

89416 

89402 

89389 

89376 

8 9 363 

8 9 35o 

89337 

89324 

89311 

89298 

89285 

89272 

89259 

89240 

89232 

89219 

89206 

89193 

89180 

89167 

89153 
8914c 
89127 
89114 

45399 

46420 

4545 i 

45477 

455 o 3 

45529 

45554 

4558o 

456o6 

45632 

45658 

45684 

45710 

46736 

46762 

46787 

46813 
46839 
45860 
45891 

46917 

46942 

46968 

45994 

46020 

46046 

46072 

46097 

46123 

46149 

46175 

46201 

46226 

46262 

46278 

46304 

4633o 

46355 

46381 

46407 

46433 

46458 

46484 

465 io 

46536 

4656 i 

46587 

46613 

46639 

46664 

46690 

46716 

46742 

46767 

46793 

46819 

46844 

46870 

40896 

46921 

89101 

89087 

89074 

89061 

89048 

89035 

89021 

89008 

88995 

88981 

88968 

88955 

88942 

88928 

88915 

88902 

88888 

88875 

88862 

88848 

88835 

88822 

88808 

88795 

88782 

88768 

88755 

88741: 

88728! 

88 7 i 5 

88701 

88688 

88674 

88661 

88647 

88634 

88620 

88607 

885 9 3 

8858o 

88566 

88553 

8853g 

88526 

885i2 

88499 

88485 
88472 
88458 
88445 
8843 i 
88417 
88404 
88390 
883 77 
88363 
88349 
88336 
8832 2 
883o8 

46947 

46973 

46999 

47024 

47050 

47076 

47101 

47127 

47i53 

47178 

47204 

47229 

47255 

47281 

473o6 

47332 

47358 

47383 

47409 

47434 

4746o 

47486 

47611 

47537 

47562 

47588 

47614 

4763 o 

47665 

47690 

47716 

47741 

47767 

47793 

47818 

47844 

47869 

47896 

47920 

47946 

47971 

47997 

48022 

48048 

48073 

48099 

48124 

48 i 5 o 

48176 

48201 

48226 

48252 

48277 

483o3 

48828 

48354 

48379 

48400 

48430 

48456 

88295 

88281 

88267 

88254 

88240 

88226 

88213 

88199 
88i85 
88172 
88158 
88144 
88i3o 
88117 
88io3 
88089 

88075 

88062 

88048 

88o34 

88020 

88006 

8799 3 

87979 

87960 

87951 

87937 

87928 

87909 

87896 

87882 

87868 

87854 

87840 

87826 

87812 

87708 

87784 

87770 

87766 

87743 

87729 

87710 

87701 

87687 

87673 

87659 

87645 

87631 

87617 

87603 

87689 

8 7 5 7 5 

87061 

87546 

87532 

8 7 5i8 

8 7 5 o 4 

87490 

87476 

48481 
485 o 6 
48532 
48557 
48583 
48608 
48634 
48659 
48684 
48710 
48735 
48761 
48786 
48811 

48887 
48862 

48888 
48913 
48938 
48964 
48989 

49014 

49040 

49066 

49090 

49116 
49U1 
49166 
49192 
49217 
49242 

49268 

49293 

49318 

49344 

49369 

49394 

49419 

49445 

49470 

49496 

49521 

49546 

49571 

49596 

49622 

49647 

49672 

49697 

49723 

40748 

49773 

49798 

49824 

49849 

49874 

49899 

49924 

49950 

49975 

87462 

87448 

87434 

87420 

87406 

87391 

87377 

87363 

87349 

87335 

87321 

87306 

87292 

87278 

87264 

87260 

87235 

87221 

87207 

87193 

87178 

87164 

87i5o 

87i36 

87121 

87107 

87093 

87079 

87064 

87060 

87036 

87021 

87007 

86993 

86978 

86964 

86949 

86936 

86921 

86906 

86892 

86878 

86863 

86849 

86834 

86820 

868o5 

86791 

86777 

86762 

86748 

86733 

86719 

86704 

86690 

86675 

86661 

86646 

86632 

86617 

M 

1 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

c. S. 1 s. 

64 Deg. 

63 Deg. 

62 Deg. 

01 Deg. 

60 Deg. 






























































































A TABLE OF NATURAL SINES, 


69 



30 Deg. 

31 Deg, 

32 Deg. 

S3 Deg. 

34 Deg. 


M 

S. 

C. S. 

■S. 

C. S. 

S. 

C.S. 

S. 

C. 8 . 

S. 

C. S. 

M 

o 

5oooo 

■866o3 

5 i 5 o 4 

85717 

52992 

84805 

54464 

8386 7 

55959 

82904 

60 

i 

5oo25 

86588 

5 i 529 

85702 

53oi7 

84789 

54488 

1 83851 

55943 

82887 

5 9 

'2 

5oo5(j 

■86673 

5 i 554 

80687 

53 o 4 i 

84774 

54013 

83835 

55968 

82871 

58 

3 

50076 

86669 

61679 

86672 

63o66 

84759 

54687 

838 m 

66992 

82855 

57 

4 

5 oioi 

86544 

51604 

86667 

53ogi 

84743 

54561 

838o', 

56oi6 

82839 

56! 

5 

5oi 26 

8653o 

61628 

85642 

53 n 5 

84728 

54586 

83 7 88 

56040 

82822 

55 

6 

5oi5i 

865i5 

51653 

86627 

53140 

84712 

54610 

83772 

66064 

82806 

54 

7 

50176 

865oi 

51678 

85612 

53164 

84697 

54635 

83756 

56o88 

82790 

53 

8 

50201 

86486 

51703 

85597 

53189 

84681 

64689 

83740 

56i 12 

82773 

62 

9 

50227 

86471 

51728 

85582 

53214 

84666 

54683 

83724 

56136 

82757 

5i 

10 

50252 

86467 

5i753 

85567 

53238 

84650 

54708 

83708 

56160 

82741 

5o 

ii 

50277 

86442 

51778 

85551 

53263 

84635 

54732 

83692 

56i84 

82724 

49 

) 12 

5 o 3 o 2 

86427 

5i8o3 

85536 

53288 

84619 

54756 

83676 

56208 

82708 

4^ 

j i3 

5 o 327 

864i3 

5i828 

85521 

533i 2 

84604 

54781 

8366o 

56232 

82692 

47 ; 

j *4 

5 o 352 

86398 

51852 

855o6 

53337 

84588 

548o5 

83645 

56256 

82675 

46 

I i5 

5 o 377 

86384 

51877 

85491 

5336i 

84573 

54829 

83629 

56280 

8265 9 

45 

| i6 

5 o 4<>3 

86369 

51902 

85476 

53386 

84557 

54854 

83613 

563o5 

82643 

44 

i 17 

50428 

86354 

51921 

86461 

53411 

84542 

54878 

83097 

5632 q 

82626 

43, 

18 

5o453 

8634o 

51962 

85446 

53435 

84526 

54902 

83581 

56353 

82610 

42 

19 

50478 

86325 

5-1977 

8543 i 

53460 

84511 

54927 

83565 

56377 

82698 

4i 

20 

5o5o3 

863 io 

52002 

86456 

53484 

84495 

64951 

83549 

564 oi 

82577 

4o 

1 21 

5o528 

86296 

52026 

85401 

53509 

84480 

54975 

83533 

56425 

82561 

3 9 

; 22 

5o553 

86281 

52 o 5 i 

85385 

53534 

84464 

54999 

83517 

56449 

82544 

38 

23 

5o578 

86766 

52076 

85370 

53558 

84448 

55o24 

835oi 

56473 

82628 

37 

24 

5o6o3 

86261 

52101 

85355 

53583 

8443 3 

55 o 48 

83485 

56497 

825 i 1 

36 

s5 

50628 

86237 

52126 

8534o 

53607 

84417 

55072 

8346 q 

565ai 

82496 

35 

26 

5o654 

86222 

62151 

85325 

53632 

84402 

55 oq 7 

83453 

56545 

82478 

34 

27 

50679 

86207 

52175 

853io 

53606 

84386 

55121 

83437 

66669 

82462 

33 

28 

50704 

86192 

52200 

86294 

5368i 

84370 

55145 

83421 

565g3 

82446 

32 

1 29 

50729 

86178 

52225 

80279 

03700 

84355 

55i6g 

834 o 5 

56617 

82429 

3i 

i 3o 

60764 

86163 

62260 

86264 

53730 

84339 

55194 

8338 9 

66641 

82413 

3o 

3i 

50779 

86148 

52275 

85249 

53754 

84324 

552i8 

833 7 3 

56665 

82396 

20] 

32 

60804 

86i33 

62299 

85234 

53779 

843o8 

55242 

83356 

5668 9 

82380 

28 

33 

50829 

86119 

52324 

85218 

538o4 

84292 

55a66 

83340 

56 7 13 

82363 

27; 

34 

5 o 854 

86104 

52349 

852 o 3 

53828 

84277 

55291 

83324 

66736 

82347 

26; 

35 

50879 

86089 

52374 

85188 

53853 

84261 

55315 

833o8 

66760 

8233 o 

25 

36 

50904 

86074 

52399 

85173 

53877 

84245 

55339 

832 9 2 

56784 

823 i 4 

24 

1 37 

50929 

86069 

62423 

85 t 57 

53902 

84230 

55363 

83276 

568o8 

82297 

23 

{ 38 

60964 

86o43 

52448 

85142 

53926 

84214 

55388 

83260 

56832 

82281 

22 

3 9 

50979 

86 g 3 o 

52473 

85i 27 

5395 i 

84198 

55412 

83244 

56856 

82264 

21 

40 

5 igo 4 

86015 

52498 

85112 

53975 

84182 

55436 

83228 

5688o 

82248 

2° | 

41 

51029 

86000 

52522 

85096 

64000 

84167 

55460 

83212 

56 9 o4 

82231 

IQ 

42 

5 io 54 

86986 

52547 

85 o 8 i 

64024 

84151 

55484 

83 i 9 5 

56928 

82214 

l8 

43 

51079 

86970 

52572 

85 o 66 

54049 

84 i 35 

55509 

83179 

56 9 52 

82198 

nj 

44 

5 i 104 

86966 

52697 

85©5 i 

64073 

84120 

55533 

83163 

56976 

82181 

16 

43 

51129 

86941 

62621 

85 o 35 

54097 

84104 

55557 

83147 

57000 

82i65 

l5 i 

46 

5i 154 

86926 

62646 

85 o 2 o 

54122 

84088 

55581 

83131 

57024 

82148 

14 

47 

51179 

85911 

62671 

85oo5 

54146 

84072 

556o5 

83115 

57047 

82132 

13 1 

43 

51204 

86896 

52696 

84989 

54171 

84057 

5563o 

83098 

57071 

82115 

12* 

49 

51229 

85881 

52720 

84974 

54195 

84041 

55654 

83o82 

57095 

82098 

11 

§0 

51264 

85866 

62745 

84969 

54220 

84026 

556 7 8 

83o66 

67119 

82082 

10 

5i 

61279 

8585i 

52770 

84943 

54244 

84009 

55702 

83o5o 

57143 

8ao65 

9 

,'52 

5i3o4 

85836 

52794 

84928 

54269 

88994 

55726 

83o34 

§7167 

8204S 

8 

53 

5 i 329 

85821 

52819 

84913 

64293 

83978 

5575o 

83oi7 

57191 

82032 

7 

54 

51354! 858o6 

52844 

84897 

54317 

88962 

55775 

83 ooi 

5721D 

82 oi 5 

6 

55 

5i 379 

85792 

52869 

84882 

54342 

88946 

55799 

82986 

57238 

81999 

6 

56 

51404 

86777 

52890 

84866 

54366 

83930 

55823 

82969 

57262 

81982 

4 

57 

61429 

86762 

52918 

84861 

54391 

83 9 i 5 

55847 

82953 

57286 

81965 

3 

58 

5i454 

85747 

52943 

84836 

54415 

838 99 

558 7 i 

82 9 36 

57310 

81949 

2 

59 

5 i 479 

85732 

52967 

84820 

54440 

83883 

558 9 5 

82920 

57334 

81932 

1 

M 

C. S. 

S. 

C. S. 1 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 


L 1 

.59 Deg. 

58 Deg. 

57 Deg. 

56 Deg. 

55 Eeg. 

-- 

















































































70 


A TABLE OF NATURAL SINES. 


M 

85 13 eg, 

3(4 Deg. 

37 Deg. 

38 Deg. 

3 $ Deg. 

! | 

S. 

I C. S. 

S. 

C. S. 

S. 

| C. S. 

S. 

e. s. 

S. 

C. S. 

M 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

IC 

11 

12 

i i 3 
| 14 

1 5 

16 

; *7 

i8 

*9 

20 

21 

22 

23 

24 

25 

26 

2 

£ 

3 1 

32 

33 
. 34 

35 

36 

37 
, 38 

39 

40 

41 

42 

43 

44 

45 

46 

47 
, 48 

49 

5 0 

5 1 

52 

53 

54 

55 

56 

5 7 

58 
; 5 9 

6735^ 

5 ) 38 ] 

5740^ 

5742c 

5745c 

pp 

67501 

5-]524 

5754^ 

57572 

57596 

67619 

57643 

67667 

57691 

57716 

57738 

57762 

57786 

67810 

57833 

57867 

5 7 88 i 

57904 

57928 

57952 

57976 

^7999 

58 o 23 

68047 

58070 

58094 
58 n 8 
58 141 
58 i 65 
58189 
58212 
58236 
68260 
58283 
583 o 7 
5833 o 
58354 
583 7 8 
584 oi 
58425 

58449 
58472 
58496 
585 19 
58543 
68067 
68090 
68614 
53637 
5866 i 
58684 
68708 
58731 
08755 

4 8191: 
81899 
81882 
81860 
81848 
8 i 832 
8181 5 
81798 
81782 
81765 
81748 
81731 
81714 

81698 

81681 

81664 

81647 

8 i 63 i 

81614 

81597 
8 i 58 o 
81 563 
8 i 546 
8 i 53 o 
81 5 1 3 
81496 

81479 

81462 

8 i 445 

81428 

8x412 

8 i 395 
81378 
8 1 36 i 

81 344 

81327 

8 i 3 io 

81293 

81276 

81269 

81242 

81225 

81208 

81191 

81174 

8 ii 5 7 

8 ii 4 o 

81123 

81106 

81089 

81072 

8 io 55 

8 io 38 

81021 

81004 

80987 

80970 

80953 

80936 

80919 

5877c 

588 o 

5882 ( 

5884 c 

588 7 C 

5889^ 

5892c 

68948 

58 o 6 - 

5899c 

69014 

59037 

69061 

59084 

5910^ 

59131 

69164 

59178 

59201 

69226 

59248 

69272 

69296 

69318 

59342 

5 9 365 

69389 

59412 

69436 

59459 

59482 

59606 

59629 

59052 

5.9576 

59599 

69622 

69646 

69669 

59693 

59716 

59739 

69763 

59786 

59809 

59832 

69856 

59879 

59902 

69926 

59949 
69972 
5 999 o 
60019 
60042 
6 oo 65 
60089 
60112; 
6 oi 35 
601 58 

> 8090: 
2 8088: 
2 80867 
) 8 o 85 c 

8 o 833 

> 80816 

> 80799 
80782 
80766 
80748 
80780 
80713 
80696 
80679 
8^602 

80644 

80627 
80610 
80593 
80576 
8 o 558 
8 o 54 i 
80624 
80507 
80489 
8047 2 
8 o 455 
8 o 438 
80420 
80403 
8 o 386 

8 o 368 

8 o 35 r 

8 o 334 

8 o 3 i 6 

80299 

80282 

80264 

80247 

8 o 23 o 

80212 

80195 

80178 

80160 

80143 

80126 

80108 
80091 
80073 
8 oo 56 
8 oo 38 
80021 
8000 3 ; 
79986 
79968 
799 51 
799^4 
79916 
79899 
79881 

.1 6018' 
>| 6020. 
1 602 2t 
J 6o20! 
6027Z 
6029c 
60821 

60344 
60367 
1 6039c 

60414 

60437 

60460 

60483 

6 o 5 o 6 

60629 

6 o 553 

60576 

60699 

60622 

60645 

60668 

60691 

60714 

60738 

60761 

60784 

60807 

6 o 83 o 

6 o 853 

60876 

60899 
60922 
60945 
60968 
60991 
6 ioi 5 
6 io 38 
61061 
61084 
61107 
61 i 3 o 
611 53 
61176 

61199 

61222 

61245 

61268 

61291 
61 3 14 
61337 
6 i 36 o 
61 383 
61406 
61429 
61451 
61474 

61497 

61020 

61543 

2 7966.' 

3 7984c? 
3 79 ^ 

79511 
i 7979 1 

79776 
79758 
79741 
797 ?3 
79706 
79688 
79671 
79653 
79635 
79618 
79600 

79583 

79565 

79547 

7953 o 

79512 
79494 
79477 
79459 
79441 
79424 
79406 
79388 
79371 
79353 
79335 

79318 

79300 

79282 

79 26 4 

79247 

79229 
79211 
79193 
79176 
791 5 S 
79 * 4 o 
79122 
79105 
79087 
79069 

79 o 5 i 

79 o 33 

79015 

78908 

78980 

78962 

78944 

78926 

78908 

78891 

78873 

78855 

78837 

78819 

6 i 56 ( 

> 61 58 c 

> 6161 
61 63 : 
61 658 
61681 
61704 
61726 
61749 

61772 

61790 

61818 

61841 

61864 

61887 

61909 

61982 

61955 

61978 

62001 

62024 
62046 
62069 
62092 
62 ii 5 
621 38 
62160 

62183 

62206 
62229 
6225 1 

62274 

62297 

62320 

62342 

62365 
62388 
62411 
62433 
62456 
62479 
62502 
62524 
62547 
62570 
62592 

62615 

62638 

62660 

62683 

62706 

62728 

62761 

62774 

62796 

62819 

62842 

62864 

62887 

62909 

> 78801 

> 78783 
1 78765 

78747 

78729 
78711 
78694 
78676 
78658 
78640 
78622 
78604 
78686 
78668 
7855 o 
78532 

785 i 4 

78496 

78478 

78460 

78442 

78424 

78406 

78387 

78369 

7835 i 

78333 

783 i 5 

78297 

78279 

78261 

78243 
78225 
78206 
78188 
78170 
78162 
78134 
78116 
78098 
78079 
78061 
78043 
78025 
78007 
77988 

77970 

77952 

77934 

77916 

77«97 

77879 

77861 

77843 

77824 

77806 

77788 

77769 

77701 

77733 

6293: 
6295 ? 
6297- 
63 00c 
63 oq: 
63 o 4 : 
63 o 6 S 
6309c 
63 'r 1C 
63 i 35 
63 1 58 
63 180 
632 oC 
63225 
63248 

63271 

6*3293 
633 16 
63338 
6336 1 
63383 
63406 
63428 
6345 1 
63473 
63496 
635 18 
6354 o 
63563 
63585 
636 o 8 

63 o 3 o 
63653 
63675 
636 9 8 
63720 
63742 
63765 
63787 
638 10 
63832 
63854 
63877 
63899 
63922 
63944 

63 c ;66 
63989 
64011 
64 o 33 
64 o 56 
64078 
64100 

64123 

641 45 
64167 
64190 

64212 

64234 

64256 

Ill 1 ' 

7769? 

> 7766c 
1 77841 
■ 77623 
7760 a 
77686 
77668 
7755 o 
7753 i 
7701 3 
77494 
77478 
77458 
77439 
77421 
77402 
77884 
77366 
77847 
77329 

773 io 

77292 

77278 

77255 

77236 

77218 

77*99 

77i8i 

77162 

77*44 

77125 

77107 

77088 

77070 

77 ° 5 i 

77 o 33 

77 oi 4 

76996 

78977 

78989 

76940 

76921 

76903 

76884 

76866 

76847 

76828 

76810 

7679* 

76772 

76754 

76735 

76717 

7669S 

76679 

76661 

76642 

76623 

> 6o| 

* 89! 

58 1 

> 87 1 
56 
55 f 
54 } 
53 1 
52 
5 i ! 
5 o| 
49 

4 $f 

47 ; 
46 f 

4>| 

44 1 

436 

42 

4 f I 

406 

39 >! 

331 

87! 

36 , 

356 

341 

33 ? 

3 ?i 

Si 

d 

a 

25 k 

2 4 

23 

22" 

21 

20 

I 8'' 

*7 ! 
165 

13 j 

14 I 

i 3 

u| 

11 1 
10 

7 ) 

6 

5 

4 

3 

2 

1 

M 

C. S. 

S. 

0. S. 

S. 

c. s. 

S. 

C. S. 

S. 

C. S. 

S. 

M 

54 Deg. 

53 Deo;. 

52 Deg. 

51 Deg. 

50 Deg. 





























































































































A TABLE OF NATURAL SINES. 


n 


C- 

1 

40 Deg. 

41 Deg. 

42 Deg. 

43 

Deg. 

44 Deg. 


\ M 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

c. s. 

S. 

C. S. 

M 

0 

64279 

76604 

656 o 6 

75471 

66918 

743 i 4 

68200 

73 i 35 

69466 

719.34 

60 

! 

643 oi 

76586 

65628 

75452 

66935 

74295 

68221 

73 ii 6 

69487 

71914 


2 

64323 

76567 

6565 o 

75433 

66956 

74276 

68242 

73096 

69608 

71894 

5$ 

3 

64346 

76548 

66672 

75414 

66978 

74206 

68264 

73076 

■ 69529 

71873 

57 

4 

64368 

7653 o 

65694 

75395 

66qqq 

74237 

68286 

73 o 56 

69549 

7 i 853 

56 

5 

64890 

76511 

66716 

75375 

67021 

74217 

683 o 6 

73 o 36 

69570 

7 i 833 

55 

6 

64412 

76492 

65738 

75356 

67043 

74108 

68327 

73 oi 6 

69591 

71813 

54 - 

/ 

6443 d 

76473 

657D9 

75337 

67064 

74178 

68349 

72996 

69612 

7 U 9 2 

53 

8 

64457 

76455 

65781 

753 i 8 

67086 

74169 

68370 

72976 

69633 

71772 

52 

; 9 

64479 

76436 

658 o 3 

75299 

67107 

74139 

68391 

72957 

69654 

71752 

5 i 

10 

645 oi 

76417 

65825 

75280 

67129 

74120 

68412 

72937 

69675 

71732 

5 o' 

11 

64524 

76398 

65847 

75261 

67161 

74100 

68433 

72917 

69696 

7 1 7 1 1 

49 

12 

64546 

76380 

6586 9 

7524 i 

67172 

74080 

68455 

72897 

69717 

71691 

48 

13 

64568 

76361 

65891 

75222 

67194 

74061 

68476 

72877 

69737 

71671 

47 

i 4 

64590 

76342 

65913 

75203 

67216 

74041 

68497 

72857 

69768 

7 i 65 o 

46 

1 i 5 

64612 

76323 

65 9 35 

75184 

67237 

74022 

685 18 

72837 

69779 

7 i 63 o 

45 

«6 

64635 

76304 

65956 

, ] 5 i 65 

67258 

74002 

6853 9 

72817 

69800 

71610 

44 

*7 

64657 

76286 

65 97 8 

75146 

67280 

73983 

6856 1 

72797 

69821 

71590 

43 

18 

64679 

76267 

66000 

75126 

67301 

73963 

68582 

72777 

69842 

71569 

42 

, *9 

64701 

76248 

66022 

75107 

67323 

73944 

686 o 3 

72757 

69862 

71549 

4 i 

,i 20 

64723 

76229 

66044 

75 o 88 

67344 

73924 

68624 

72737 

69883 

71629 

40; 

21 

64746 

76210 

66066 

75 o 6 g 

67366 

73904 

68645 

72717 

69904 

7 i 5 o 8 

3 9 i 

22 

64768 

76192 

66088 

"j 5 o 5 o 

67387 

73885 

68666 

72697 

69925 

71488 

381 

23 

64790 

76173 

66109 

, j 5 o 3 o 

67409 

73865 

68688 

72677 

69946 

71468 

37 

24 

64812 

76154 

661 3 1 

75 oi 1 

6743 o 

73846 

68709 

72657 

69966 

71447 

36 

25 

64834 

76 i 35 

661 53 

74992 

67462 

73826 

68730 

72637 

69987 

71427 

35 ; 

26 

64856 

76116 

66175 

74973 

67473 

73806 

68761 

72617 

70008 

71407 

34 

27 

64878 

76097 

66197 

74953 

67495 

78787 

68772 

72697 

70029 

7 i 386 

33 

28 

64901 

76078 

66218 

74934 

67516 

73767 

68793 

72577 

70049 

7 1 366 

32 

29 

64923 

76059 

66240 

749 i 5 

67538 

73747 

68814 

72557 

70070 

7 i 345 

3 i 

3 o 

64945 

76041 

66262 

74896 

67559 

73728 

68835 

72537 

70091 

71 3 25 

3 ° 

3 i 

64967 

76022 

66284 

74876 

67580 

73708 

68857 

72517 

70112 

7 i 3 o 5 

29 

32 

64989 

76003 

663 o 6 

74857 

67602 

73688 

68878 

72497 

70132 

71284 

28 

33 

65 oi i 

75984 

66327 

74838 

67623 

73669 

68899 

72477 

7 oi 53 

71264 

27 i 

34 

65 o 33 

75965 

66349 

74818 

67645 

73649 

68920 

72467 

70174 

71243 

26; 

35 

65 o 55 

75946 

66371 

74799 

67666 

73629 

68941 

72437 

70195 

71223 

25 

36 

65077 

75927 

663 g 3 

74780 

67688 

73610 

68962 

72417 

7021 5 

71203 

24; 

37 

6 5099 

76908 

66414 

74760 

67709 

73590 

6898J 

72397 

70236 

71182 

23 

38 

65 122 

76889 

66486 

74741 

67730 

73570 

69004 

72377 

70267 

71162 

2 2 

39 

65 144 

75870 

66468 

74722 

67752 

7355 i 

69026 

72357 

70277 

7 ii 4 i 

21 

40 

65 166 

7585 1 

66480 

747 o 3 

67773 

7 353 1 

69046 

72337 

70298 

71121 

20 

4 i 

65 188 

7 5832 

665 oi 

74683 

67795 

735 ii 

69067 

72317 

70319 

71100 

19 

42 

652 io 

7 58 i 3 

66523 

74664 

67816 

73491 

69088 

72297 

70339 

71080 

18; 

43 

65232 

7^794 

66548 

74644 

67837 

73472 

69109 

72277 

7 o 36 o 

71069 

17 

44 

65254 

75775 

66566 

74625 

67859 

73452 

6 qi 3 o 

72257 

7 o 38 i 

71039 

16 

45 

65276 

75756 

66588 

74606 

67880 

73432 

69161 

72236 

70401 

71019 

id" 

46 

65298 

75738 

66610 

74586 

67901 

73412 

69172 

72216 

70422 

70998 

14 

47 

65320 

75719 

66632 

74567 

67923 

73393 

69193 

72196 

70443 

70978 

i 3 

48 

65342 

76699 

66653 

74548 

67944 

73373 

69214 

72176 

70463 

70957 

12; 

49 

65364 

75680 

66675 

74528 

67965 

73353 

69286 

721 56 

70484 

70937 

11 

5 o 

65386 

75661 

66697 

74509 

67987 

73333 

69266; 

721 36 

7 o 5 o 5 

70916 

10} 

5 i 

654 o 8 

75642 

66718 

74489 

68008 

733 i 4 

69277! 

72116 

7 o 525 

70896 

9j 

52 

6543 o 

75623 

66740 

7447 ° 

68029 

73294 

69298 

72095 

70546 

70875 

8] 

53 

65452 

76604 

66762 

7445 i 

68 o 5 i 

73274 

69319 

72075 

70667 

7 o 855 

7 i 

54 

65474 

7 5585 

66783 

7443 i 

68072 

73264 

69340 

72 o 55 

70587 

70834 

6 

1 55 

65496 

75566 

668 o 5 

74412 

68093 

73234 

69361 

72 o 35 

70608 

70813 

5 

56 

655 1 8 

75547 

66827 

74392 

6811 5 

7321.5 

69382 

72015 

70628 

70793 

4 

1 5 7 

6554 o 

75528 

66848 

74373 

68 1 36 

73195 

69403 

71995 

70649 

70772 

3 

j 58 

65 d 62 | 

75609 

66870 

74353 

68167 

73175 

69424 

71974 

70670 

70762 

2 


65584 

75490 

66891 

74334 

68179 

73 1 55 

69445 

71904 

70690 

70731 

1 

! 60 

656 o 6 

76471 

66913 

743 i 4 

68200 

73 1 35 

69466 

71934 

70711 

707 11 

0 

i m 

cTsr 

S. 

C. S. 

S. 

C. S. 

S.. 

c. s. 

S. 

C. S. 

S. 

M 

_ 

49 Deg. * 

48 Deg. 1 

47 Deg. 

46 Deg. 

45 Deg. 

t 






































































































2 


Til x VERSE TAHLF, 


o 

*"*• 

a 

r“*- 

PA 

3 

O 

p 

\ Deg. 

i 

Deg. 

3 Deg. 

Distance.] 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

} 

1.00 

0.00 

1.00 

0.01 

1.00 

0.01 

1 

a 

2.00 

0.01 

2.00 

0.02 

2.00 

0.03 

2 

3 

3.00 

0.01 

3 . 00 

0.03 

3.00 

0.04 

3 

4 

4.00 

0.02 

4.00 

0.03 

4.00 

0.05 

4 

ft 

ft. 00 

0.02 

5.00 

0.04 

5.00 

0.07 

5 

6 

6.00 

0.03 

6.00 

0.05 

6.00 

0 08 

6 

7 

7.00 

0.03 

7.00 

0.06 

7.00 

0.09 

7 

8 

8.00 

0.03 

8.00 

0.07 

8.00 

0.10 

8 

9 

9.00 

0.04 

9.00 

0.08 

9.00 

0.12 

9 

JO 

10.00 

0.04 

10.00 

0.09 

10.00 

0.13 

10 

11 

11.00 

0.05 

11.00 

0.10 

11.00 

0.14 

11 

12 

12.00 

0.05 

12.00 

0.10 

12.00 

0.16 

12 

13 

13.00 

0.06 

13.00 

0.11 

13.00 

0. 17 

13 

14 

14.00 

0.06 

14.00 

0 . 12 

14.00 

0.18 

14 

15 

15.00 

0.07 

15.00 

0.13 

15.00 

0.20 

15 

16 

16.00 

0.07 

16.00 

0.14 

16.00 

0.21 

16 

17 

17.00 

0.07 

17.00 

0.15 

17.00 

0.22 

17 

18 

18.00 

0 08 

18 00 

0 . 16 

18.00 

0.24 

18 

19 

19.00 

0.08 

19.00 

0.17 

19.00 

0.25 

19 

20 

20.00 

0.09 

20.00 

0.17 

20.00 

0.26 

20 

21 

21.00 

0.09 

21.00 

0.18 

21.00 

0.27 

21 

22 

22.00 

0.10 

22.00 

0.19 

22.00 

0.29 

22 

23 

23.00 

0.10 

23.00 

0.20 

23.00 

0.30 

23 

24 

24.00 

0.10 

24.00 

0.21 

24.00 

0.31 

24 

25 

25.00 

0.11 

25.00 

0.22 

25.00 

0.33 

25 

26 

26.00 

0.11 

26.00 

0.23 

26.00 

0.34 

26 

27 

27.00 

0.12 

27.00 

0.24 

27.00 

0.35 

27 

28 

28.00 

0.12 

28.00 

0.24 

28.00 

0.37 

28 

29 

29.00 

0.13 

29.00 

0.25 

29.00 

0.38 

29 

30 

30.00 

0.13 

30.00 

0.26 

30.00 

0.39 

30 

31 

31.00 

0.14 

31.00 

0.27 

31.00 

0.41 

31 

32 

32.00 

0.14 

32.00 

0.28 

32.00 

0.42 

32 

33 

33.00 

0.14 

33.00 

0-29 

33.00 

0.43 

33 

34 

34.00 

0.15 

34.00 

0.30 

34.00 

0.45 

34 

35 

35.00 

0.15 

35.00 

0.31 

35.00 

0.46 

35 

36 

36.00 

0.16 

36.00 

0.31 

36.00 

0.47 

36 

37 

37.00 

0.16 

37.00 

0.32 

37.00 

0.48 

37 

38 

38.00 

0.17 

38.00 

0.33 

38.00 

0.50 

38 

39 

39.00 

0.17 

39.00 

0.34 

39.00 

0.51 

39 

40 

40.00 

0.17 

40.00 

0.35 

40.00 

0.52 

40 

41 

41.00 

0.18 

41.00 

0.36 

41.00 

0.54 

41 

42 

42.00 

0.18 

42.00 

0.37 

42.00 

0.55 

42 

43 

43.00 

0.19 

43.00 

0.38 

43.00 

0.56 

43 

44 

44.00 

0.19 

44.00 

0.38 

44.00 

0.58 

44 

, 4ft 

45.00 

0.20 

45.00 

0.39 

45.00 

0.59 

45 

1 46 

46.00 

0,20 

46.00 

0.40 

46.00 

0.60 

46 

47 

47.00 

0.21 

47.00 

0.41 

47.00 

0.62 

47 

4-8 

48.00 

0.21 

48.00 

0.42 

48.00 

0.63 

48 

49 

49.00 

0.21 

49.00 

0.43 

49.00 

0.64 

49 

50 

50.00 

0.22 

50.00 

0.44 

50.00 

0.65 

50 

1 | 

* Distance. 

* 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance.j 

89| Deg. 

89 £ 

Deg. 

89$ Deg. 




























































































TKAVEltSE TAULE. 


3 


A 


Distance. J 

1 _' 

} Deg. 

h Deg. 

1 Deg. 

Distance.! 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

r 

Dep. 

51 

51.00 

0.22 

51.00 

0.45 

51.00 

0.67 

51 

52 

52.00 

0.23 

52.00 

0.45 

52.00 

0.68 

52 

53 

53.00 

0.23 

53.00 

0.46 

53.00 

0.69 

53 

54 

54.00 

0.24 

54.00 

0.47 

54.00 

0.71 

| 54 

55 

55.00 

0.24 

55.00 

0.48 

55.00 

0.72 

55 

56 

56.00 

0.24 

56.00 

0.49 

56.00 

0.73 

56 

5 ? 

57.00 

0.25 

57.00 

0.50 

57.00 

0.75 

57 

58 

58.00 

0.25 

58.00 

0.51 

57.99 

0.76 

58 

59 

59.00 

0.26 

59.00 

0.51 

58.99 

0.77 

59 

60 

60.00 

0.26 

60.00 

0.52 

59.99 

0.79 

60 

61 

61.00 

0.27 

6i .00 

0.53 

60.99 

0.80 

61 

62 

62.00 

0.27 

62.00 

0.54 

61.99 

0.81 

62 

63 

63.00 

0.27 

63.00 

0.55 

62.99 

0.82 

63 

64 

64.00 

0.28 

64.00 

0.56 

63.99 

0.84 

64 

65 

65.00 

0.28 

65.00 

0.57 

64.99 

0.85 

65 

66 

66.00 

0.29 

66.00 

0.58 

65.99 

0.86 

66 

67 

67.00 

0.29 

67.00 

0.58 

66.99 

0.88 

67 

68 

68.00 

0.30 

68.00 

0.59 

67.99 

0.89 

68 

69 

69.00 

0.30 

69.00 

0.60 

68.99 

0.90 

69 

70 

70.00 

0.31 

70.00 

0.61 

69.99 

0.92 

70 

71 

71.00 

0.31 

71.00 

0.62 

70.99 

0.93 

71 

72 

72.00 

0.31 

72.00 

0.63 

71.99 

0.94 

72 

73 

73.00 

0.32 

73.00 

0.64 

72.99 

0.96 

73 

74 

74.00 

0.32 

74.00 

0.65 

73.99 

0.97 

74 

75 

75.00 

0.33 

75.00 

0.65 

74.99 

0.98 

75 

76 

76.00 

0.33 

76.00 

0.66 

75.99 

0.99 

76 

77 

77.00 

0.34 

77.00 

0.67 

76.99 

1.01 

77 

78 

78.00 

0.34 

78.00 

0.68 

77.99 

1.02 

78 

79 

79.00 

0.34 

79.00 

0.69 

78.99 

1.03 

79 

80 

80.00 

0.35 

80.00 

0.70 

79.99 

1.05 

80 

"81 

81.00 

0.35 

81.00 

0.71 

80.99 

1.06 

81 

82 

82.00 

0.36 

82.00 

0.72 

81.99 

1.07 

82 

83 

83.00 

0.36 

83.00 

0.72 

82.99 

1.09 

83 

84 

84.00 

0.37 

84.00 

0.73 

83.99 

1.10 

84 

85 

65.00 

0.37 

85.00 

0.74 

84.99 

1.11 

85 

86 

86.00 

0.38 

86.00 

0.75 

85.99 

1.13 

86 

87 

87.00 

0.38 

87.00 

0.76 

86.99 

1.14 

87 

88 

88.00 

0.38 

88.00 

0.77 

87.99 

1.15 

88 

89 

89.00 

0.39 

89.00 

0.78 

88.99 

1.16 

89 

90 

90.00 

0.39 

90.00 

0.79 

89.99 

1.18 

90 

91 

91.00 

0.40 

91.00 

0.79 

90.99 

1.19 ! 

91 

92 

92.00 

0.40 

92.00 

0.80 

91.99 

1.20 

92 

93 

93.00 

0.41 

93.00 

0.81 

92.99 

1.22 

93 

94 

94.00 

0.41 

94.00 

0.82 

93.99 

1.23 

94 

95 

95.00 

0.41 

95.00 

0.83 

94.99 

1.24 

95 

96 

96.00 

0.42 

96.00 

0.84 

95.99 

1.26 

96 

97 

97.00 

0.42 

97.00 

0.85 

96.99 

1.27 

97 

98 

98.00 

0.43 

98.00 

0.86 

97.99 

1.28 

98 

99 

99.00 

0.43 

99.00 

0.86 

98.99 

1.30 

99 

100 

100.00 

0.44 

100.00 

0.87 

99.99 

1.31 

100 

6 

o 

C 

rt 

CO 

G 

_ 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

89 ] Deg. 

i 

89£ Deg. 

89} Deg. 












































































4 


TRAVERSE TABJLE 


1 Distance. 

j 

1 Deg. 

H Deg. 

L; 

l£ Deg 



Deg. 

Distance. | 
1 

Lat. 

Dep. 

Lat. 

Dep. 

it. | 

i 

D• 

Lat. 

Dep. 

1 

1.00 

0.02 

1. 

00 

0.02 

~ 1 

00 

0 


1 . DU 

0.03 

1 

2 

2.00 

0.03 

2. 

00 

0.04 

2 

DU 

/ 

(,r 1 

2.00 

0.06 ‘ 

2 

3 

3.00 

0.05 

3. 

00 

0.07 

1 

'iU 

(t 

fry 

3.00 

0 09 

3 

4 

1.00 

0.07 

4. 

00 

0.09 


0 4 

u 

TO 

4.00 

0.12 

4 

5 

5.00 

0.09 

5. 

00 

0.11 

5 

00 

'> 

.13 

5.00 

0.15 

5 

6 

6.00 

0.10 

6. 

00 

0. 13 

6 

' 0 

u 

.16 

6.00 

0 18 

6 

7 

7.00 

0.12 

7. 

00 

0.15 

7. 

06 

f\ 

.13 

7,00 

0.21 

7 

8 

8.00 

0.14 

8. 

00 

0. 17 | 

8 

00 

0 

21 

8.00 

0.25 

8 

9 

9.00 

0.16 

9 

00 

0.20 

9. 

00 

0 

24 

9.0^ 

0.23 

9 

10 

10.00 

0 17 

10 

00 

0.22 

10 

00 

0 

26 

10.00 

0.31 

10 

1 l 

11.00 

0.19 

J 1 

00 

0.24 

1 1 

00 

0 

28 

10.99 

0.34 

11 

12 

12.00 

0.21 

12 

00 

0.26 

12 

00 

0 

31 

11.99 

0.37 

12 

13 

13.00 

0.23 

13 

00 

0.28 

13 

00 

0 

34 

12.99 

0.40 

13 

14 

14.00 

0.24 

14 

00 

0.31 

14. 

00 

0 

37 

13.99 

0.43 

14 

15 

15.00 

0.26 

15 

00 

0.33 

14. 

99 

0 

39 

14.99 

0.46 

i5 

16 

16.00 

0.28 

16 

00 

0.35 

15. 

99 

0 

42 

15.99 

0.49 

16 

17 

17.00 

0.30 

17 

00 

0.37 

16. 

99 

0 

45 

16.99 

0.52 

17 

18 

18.00 

0.31 

18 

00 

0.39 

17. 

99 

0 

47 

17.99 

0.55 

18 

19 

19.00 

0.33 

19 

00 

0.41 

18. 

99 

0 

50 

18.99 

0.58 

19 

20 

20.00 

0.35 

20 

00 

0.44 

19. 

99 

0 

52 

19.99 

0.61 

20 

21 

21.00 

0.37 

21 

00 

0.46 

20. 

99 

0. 

55 ! 

20.99 

0.64 

21 

22 

22.00 

0.38 

21 

99 

0.48 

21. 

99 

0 

58 

21.99 

0.67 

22 

23 

23.00 

0.40 

22 

99 

0.50 

22. 

99 

0 

60 

22.99 

0.70 

23 

24 

24.00 

0.42 

23 

99 

0.52 

23. 

99 

0 

63 

23.99 

0.73 

24 

25 

25.00 

0.44 

24 

99 

0.55 

24, 

99 

0 

65 

24.99 

0.76 

25 

26 

26.00 

0.45 

25 

99 

0.57 

25. 

99 

0 

68 

25.99 

0.79 

26 

27 

27.00 

0.47 

26 

99 

0 59 

26. 

99 

0 

.71 

26.99 

0.83 

27 

28 

28.00 

0.49 

27 

.99 

0.61 

27. 

99 

0 

.73 

27.99 

0.86 

28 

29 

29.00 

0.51 

28 

99 

0.63 

28 

99 

0 

.76 

28.99 

0.89 

29 

30 

30.00 

0.52 

29 

.99 

0.65 

29 

99 

0 

.79 

29.99 

0.92 

30 

31 

31.00 

0.54 

30 

99 

0.68 

30 

99 

0 

.81 

30.99 

0.95 

31 

32 

32.00 

0.56 

31 

99 

0.70 

31 

.99 

0 

.84 

31.99 

0.98 

32 

33 

32.99 

0.58 

32 

99 

0.72 

32 

.99 

0 

.86 

32.98 

1.01 

33 

34 

33.99 

0.59 

33 

99 

0.74 

33 

.99 

0 

.89 

33.98 

1.04 

34 

35 

34.99 

0.61 

34 

99 

0.76 

34 

.99 

0 

.92 

34.93 

1.07 

35 

36 

35.99 

0.63 

3d 

.99 

0.79 

35 

.99 

0 

.94 

35.93 

1.10 

36 

37 

36.99 

0.65 

36 

.99 

0.81 

36 

.99 

0 

.97 

36.98 

1.13 

37 

38 

37.99 

0.66 

37 

.99 

. 0.83 

37 

.99 

0 

.99 

37.98 

1.16 

38 

39 

38.99 

0.68 

38 

.99 

0.85 

38 

.99 

1 

.02 

38.98 

1.19 

39 

40 

39.99 

0.70 

39 

.99 

0.87 

39 

.99 

1 

.05 

39.98 

] .22 

40 

41 

40.99 

0.72 

40 

.99 

0.89 

40 

.99 

1 

.07 

i40.98 

1 25 

‘41 

42 

41.99 

0.73 

41 

.99 

0.92 

41 

.99 

1 

.10 

41.98 

1 28 

i 42 

43 

42.99 

0.75 

42 

.99 

0.94 

42 

.99 

1 

.13 

42.98 

1.31 

! 43 

44 

43.99 

0.77 

43 

.99 

0.96 

43 

.99 

1 

.15 

43.98 

1.84 

14 

45 

44.99 

0.79 

44 

.99 

0.98 

44 

.99 

1 

.18 

44.98 

1.37 

45 

46 

45.99 

0.80 

45 

.99 

1.00 

45 

.99 

1 

.20 

45.98 

1.40 

46 

47 

46.99 

0.82 

46 

.99 

1.03 

46 

.99 

1 

.23 

46.98 

1.44 

47 

48 

47.99 

0.84 

47 

.99 

1.05 

47 

.98 

1 

.26 

47.98 

1.47 

48 

49 

48.99 

0.86 

48 

.99 

1.07 

48 

.98 

l 

.28 

48.98 

1.50 

49 

50 

49.99 

0.87 

49 

.99 

1.09 

49 

.98 

1 

.31 

149.98 

1.53 

50 

© 

O 

G 

cd 

<-» 

co 

• H 

G 

Dep. 

Lat. 

Dep. 

Lilt. 

Dep. 

Lat 

Dep. 

Lat. 

© 

o 

c 

cd 

C/3 

• 

3 

89 Deg. 

88| Deg. 


88i 

De 

g- 

88J Deg. 

I 












































































































Distance.! © «0 tO CD CO CO CO CO CD CO I CO 00 00 00 00 00 OO 00 00 OO OO O *<f <J V! <! <»©©©©©©©©© ©©tntnOiCJi©Cntn £?v .niTraioi^T 

l©©QD'v!©U'i^C0Wr-i©©00<j©Oi>l i -C0K!t—l©©O0^©m^COK)i-' ©CDQO<!a>a'^iitS>— ©(OOO^OO'^WM-' aOUKJSfQ 


TRAVERSE TABLE 


o 


1 

1 Deg. ! 

i 

\\ Deg. 

H Deg. 

1! Deg. 

U 

• 

r Jl 

1 —* 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 Dep. 

Lat. 

Dep. 

3 

O 

CD 

50.99 

0.89 

50.99 

1.11 

50.98 

1.34 

■50798 

1.56 

5] 

51,99 

0.91 

51.99 

1.13 

51.88 

52.98 

1.36 

51.98 

1.59 

52 

52 99 

0.92 

52.99 

1.16 

1.39 

52.98 

1.62 

53 

53 99 

0.94 

53.99 

1.18 

53.98 

1.41 

53.97 

1.65 

51 

54. 99 

0.96 

54.99 

1.20 

54.98 

1.44 

54.97 

1.68 

55 

5.5.99 

0.98 

55.99 

1.22 

55.98 

1.47 

55.97 

1.71 

56 

56.99 

0.99 

56.99 

1.24 

56 98 

1.49 

56.97 

1.74 

57 

57.99 

1.01 

57.99 

1.27 

57.98 

1.52 

57.97 

1.77 

58 

58.99 

1.03 

58.99 

1.29 

58.98 

1.54 

58.97 

1.80 

59 

59.99 

1.05 

59.99 

1.31 

59.98 

1.57 

59.97 

1.83 

60 

60.99 

1.06 

60.99 

1.33 

60.93 

1.60 

60.97 

1.86 

61 

61.99 

1.08 

'61.99 

1.35 

61.93 

1.62 

61.97 

1.89 

62 

62.99 

1.10 

62.99 

1.37 

62.98 

1.65 

62.97 

1.92 

63 

63.99 

1.12 

63.98 

1.40 

6.3.93 

1.68 

63.97 

1.95 

64 

64.99 

1.13 

64.98 

1.42 

64.98 

1.70 

64.97 

1.99 

65 

65.99 

1.15 

65.98 

1.44 

85.98 

1.73 

65.97 

2.02 

66 

66.99 

1.17 

66.98 

1.46 

66.98 

1.75 

66.97 

2.05 

67 

67.99 

1.19 

67.98 

1.48 

67.98 

1.78 

67.97 

2.08 

68 

68.99 

1.20 

68.98 

1.51 

68.98 

1.81 

68 97 

2.11 

69 

69.99 

1.22 

69.98 

1.53 

69.98 

1.83 

69-97 

2.14 

70 

70.99 

1.24 

70.98 

1.55 

70.98 

1.86 

70.97 

2.17 

71 

71.99 

1.26 

71.98 

1.57 

71.98 

1.88 

71.97 

2.20 

72 

72.99 

1.27 

72.98 

1.59 

72.97 

1.91 

72.97 

2.23 

73 

73.99 

1.29 

73.98 

1.61 

73.97 

1.94 

73.97 

2.26 

74 

74.99 

1.31 

74.98 

1.64 

74.97 

1.96 

74.97 

2.29 

75 

75.99 

1.33 

75.98 

1.66 

75.97 

1.99 

75.96 

2.32 

76 

76.99 

1.34 

76.98 

1.68 

76.97 

2.02 

76.96 

2.35 

77 

77.99 

1.36 

77.98 

1.70 

77.97 

2.04 

77.96 

2.38 

78 

78.99 

1.38 

78.98 

1.72 

78.97 

2.07 

78.96 

2.41 

79 

79.99 

1.40 

79.98 

1.75 

79.97 

2-09 

79.96 

2.44 

80 

80.99 

I .41 

80.98 

1.77 

80.97 

2.12 

80.96 

2.47 

81 

81.99 

1 .43 

81.98 

1.79 

81.97 

2.15 

81.96 

2.50 

82 

82.99 

1.45 

82.98 

1.81 

82.97 

2.17 

82.96 

2.53 

83 

83.99 

1.47 

83.98 

1.83 

83.97 

2.20 

83.96 

2.57 

84 

84.99 

1 .48 

84.98 

1.85 

84.97 

2.23 

84.96 

2.60 

85 

85.99 

1.50 

85.98 

1.88 

85.97 

2.25 

85.96 

2.63 

86 

86.99 

1.52 

86.98 

1.90 

86.97 

2.28 

86.96 

2.66 

87 

87.99 

1.54 

87.98 

1.92 

87.97 

2.30 

87.96 

2.69 

88 

88.99 

1.55 

88.98 

1.94 

88.97 

2.33 

88.96 

2.72 

89 

89.99 

1.57 

89.98 

1.96 

89.97 

2.36 

89.96 

2.75 

90 

90.99 

1.59 

90.98 

1.99 

90.97 

2.38 

90.9b 

' 2.78 

91 

91.99 

1.61 

91 98 

2.01 

91. or 

2.41 

91 .96 

2.81 

92 

92.99 

1.62 

92.98 

2.03 

92.9' 

2.43 

92.96 

2.84 

93 

93.99 

1.64 

93.98 

2.05 

93.97 

2.46 

93.96 

2.87 

94 

94.99 

1.66 

94.98 

2.07 

94.97 

2.49 

94.96 

2.90 

95 

95 ,99 

1.68 

95.98 

2.09 

95.97 

2.51 

95.96 

2.94 

96 

96.99 

1.69 

96.98 

2.12 

96.97 

2.54 

96.95 

2.96 

97 

97.99 

1.71 

97.98 

2.14 

97.97 

2.57 

97.95 

2,99 

98 

98.98 

1.73 

98.98 

2.16 

98.97 

2.59 

98.95 

3 02 

9J 

99.98 

1.75 

99.98 

2.18 

99.97 

2.62 

99.95 

3.05 

10(1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

Lat. 

Dep. 

j L» 1 

0) 

« 

g 

89 Deg. 

88! Deg. 

88i Deg. 

i 

88! De£ 

CD 

11 

JU 






















































































TRAVERSE TARLE. 


0 


Distance.j 

2 Deg. 

24 Deg. 

Deg.. 

Deg. 

Distance.j 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

Lat. 

Dep. 

1 

1.00 

0 

.03 

1.00 

0.04 

1.00 

0.04 

1.00 

0.05 

1 

2 

2.00 

0 

.07 

2.00 

0.08 

2.00 

0.09 

2.00 

0.10 

2 

3 

3.00 

0 

.10 

3.00 

0.12 

3.00 

0.13 

3.00 

0.14 

3 

4 

4.00 

0 

.14 

4.00 

0.16 

4.00 

0.17 

4.00 

0.19 

4 

5 

5.00 

0 

17 

5.00 

0.20 

5.00 

0.22 

4.99 

0.24 

5 

6 

6.00 

0 

.21 

6.00 

0.24 

5.99 

0.26 

5.99 

0.29 

6 

7 

7.00 

0 

.24 

6.99 

0.27 

6.99 

0.31 

6.99 

0.34 

7 

8 

7.99 

0 

.28 

7.99 

0.31 

7.99 

0.35 

7.99 

0.38 

8 

9 

8.99 

0 

.31 

8.99 

0.35 

8.99 

0.39 

8.99 

0.43 

9 

10 

9.99 

0 

.35 

9.99 

0.39 

9.99 

0.44 

9.99 

0.48 

10 

11 

10.99 

0 

.38 

10.99 

0.43 

10.99 

0.48 

10.99 

0.53 

11 

12 

11.99 

0 

.42 

11.99 

0.47 

11.99 

0.52 

11.99 

0.58 

12 

13 

12.99 

0 

.45 

12.99 

0.51 

12.99 

0.57 

12.99 

0.62 

13 

14 

13.99 

0 

.49 

13.99 

0.55 

13.99 

0.61 

13.98 

0.67 

14 

15 

14.99 

0 

.52 

14.99 

0.59 

14.99 

0.65 

14.98 

0.72 

15 

16 

15.99 

0 

.56 

15.99 

0.63 

15.99 

0.70 

15.98 

0.77 

16 

17 

16.99 

0 

59 

16.99 

0.67 

16.98 

0.74 

16.98 

0.82 

17 

18 

17.99 

0 

.63 

17.99 

0.71 

17.98 

0.79 

17.98 

0.86 

18 

19 

18.99 

0 

.66 

18.99 

0.75 

18.98 

0.83 

18.98 

0.91 

19 

20 

19.99 

0 

.70 

19.98 

0.79 

19.98 

0.87 

19.98 

0.96 

20 

21 

20.99 

0 

.73 

20.98 

0.82 

20.98 

0.92 

20.98 

1.01 

21 

22 

21.99 

0 

.77 

21.98 

0.86 

21.98 

0.96 

21.97 

1.06 

22 

23 

22.99 

0 

.80 

22.98 

0.90 

22.98 

1.00 

22.97 

1.10 

23 

24 

23.99 

0 

.84 

23.98 

0.94 

23.98 

1.05 

23.97 

1.15 

24 

25 

24.98 

0 

.87 

24.98 

0.98 

24.98 

1.09 

24.97 

1.20 

25 

26 

25.98 

0 

.91 

25.98 

1.02 

25.98 

1.13 

25.97 

1.25 

26 

27 

26.98 

0 

.94 

26.98 

1.06 

26.97 

1.18 

26.97 

1.30 

27 

28 

27.98 

0 

.98 

27.98 

1.10 

27.97 

1.22 

27.97 

1 .34 

28 

29 

28.98 

1 

.01 

28.98 

1.14 

28.97 

1.26 

23.97 

1.39 

29 

30 

29.98 

1 

.05 

29.98 

1.18 

29.97 

1.31 

29.97 

1 .44 

30 

31 

30.98 

1 

.08 

30.98 

1.22 

30.97 

1.35 

30.96 

1.49“ 

31 

32 

31.98 

1 

.12 

31.98 

1.26 

31.97 

1.40 

31.96 

1.54 

32 

33 

32.98 

1 

.15 

32.97 

1.30 

32.97 

1.44 

32.96 

1.58 

33 

34 

33.98 

1 

.19 

33.97 

1.33 

33.97 

1.48 

33.96 

1.63 

34 

35 

34.98 

1 

.22 

34.97 

1.37 

34.97 

1.53 

34.96 

1.68 

35 

36 

35.98 

1 

.26 

35.97 

1.41 

35.97 

1.57 

35.96 

1.73 

36 

37 

36.98 

1 

.29 

36.97 

1.45 

36.96 

1.61 

36.96 

1.78 

37 

38 

37.99 

1 

.33 

37.97 

1.49 

37.96 

1.66 

37.96 

1.82 

38 

39 

38.98 

1 

.36 

38.97 

1.53 

38.96 

1.70 

38.96 

1.87 

39 

40 

39.98 

1 

.40 

39.97 

157 

39.96 

1.75 

39.95 

1.92 

40 

41 

40.98 

1 

.43 

40.97 

1.61 

40.96 

1.77 

40.95 

1.97 

41 

42 

41.97 

1 

.47 

41.97 

1.65 

41.96 

1.83 

41.95 

2.02 

42 

43 

42.97 

1 

.50 

42.97 

1.69 

42.96 

1.88 

42.95 

2.06 

4 3 

44 

43.97 

1 

.54 

43.97 

1.73 

43.96 

1.92 

43.95 

2.11 

44 

45 

44.97 

1 

.57 

44.97 

1.77 

44.96 

1.96 

44.95 

2.16 

45 

46 

45.97 

1 

.61 

45.96 

1.81 

45.96 

2.01 

45.95 

2.21 

46 

47 

146.97 

1 

.64 

46.96 

1.85 

46.96 

2.05 

46.95 

2.25 

47 

48 

'47.97 

1 

.68 

47.96 

1.88 

47.95 

2.09 

47.95 

2.30 

48 

49 

j 48.97 

1 

.71 

48.96 

1.92 

48.95 

2.14 

48.94 

2.35 

49 

50 

;49.97 

1 

.74 

49.96 

1.96 

49.95 

2.18 

49.94 

2.40 

50 

• 

o 

o 

c 

CCS 

m 
• •—< 

1 Dcp 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance.| 

88 Deg. 

871 Deg. 

87± 

Deg. 

87} Deg. 
























































































THAVERSE TABLE. 


7 


o 

M ' 

01 

r-* 

P 

i 

2 Deg. 

i 

2$ Deg. 

94. 

Deg. 

2 1 Deg. 

U 

p~ • 

to 

P 

3 

O 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

3 

_ 1 

51 

50.97 

1.78 

50.96 

2.00 

50.95 

2.22 

50.94 

2.45 

51 

52 

51.97 

1.81 

51.96 

2.04 

51.95 

2.27 

51.94 

2.50 

52 

53 

52.97 

1.85 

52.96 

2.08 

52.95 

2.31 

!52.94 

2.54 

53 

54 

i 53.97 

1.88 

53.96 

2.12 

53.95 

2.36 

53.94 

2.59 

54 

55 

54.97 

1.92 

54.96 

2.16 

54.95 

2.40 

54.94 

2.64 

55 

56 

! 55.97 

1.95 

55.96 

2.20 

55.95 

2.44 

55.94 

2 69 

56 

57 

|56.97 

1.99 

56.96 

2.24 

56.95 

2.49 

56.93 

2.73 

57 

58 

157.96 

2.02 

57.96 

2.28 

57.94 

2.53 

57.93 

2.78 

58 

59 

'58.96 

2.06 

58.95 

2.32 

58.94 

2.57 

58.93 

2.83 

59 

60 

59.96 

2.09 

59.95 

2.36 

59.94 

2.62 

59.93 

2.88 

60 

61 

60.96 

2.13 

60,95 

2.39 

60.94 

2.66 

60.93 

2.93 

61 

62 

61.96 

2.16 

61.95 

2.43 

61.94 

2.70 

61.93 

2.97 

62 

63 

62.96 

2.20 

62.95 

2.47 

62.94 

2.75 

62.93 

3.02 

63 

64 

63.96 

2.23 

63.95 

2.51 

63.94 

2.79 

63.93 

3.07 

64 

65 

64.96 

2.27 

64.95 

2.55 

64.94 

2.84 

64.93 

3.12 

65 

66 

65.96 

2.30 

65.95 

2.59 

65.94 

2.88 

65.92 

3.17 

66 

67 

66.96 

2.34 

66.95 

2.63 

66.94 

2.92 

66.92 

3.21 

67 

68 

67.96 

2.37 

67.95 

2.67 

67.94 

2.97 

67.92 

3.26 

68 

69 

68.96 

2.41 

68.95 

2.71 

68.93 

3.01 

68.92 

3.31 

69 

70 

69.96 

2.44 

69.95 

2.75 

69.93 

3.05 

69.92 

3.36 

70 

71 

70.96 

2.48 

70.95 

2.79 

70.93 

3.10 

70.92 

3.41 

71 

72 

71.96 

2.51 

71.94 

2.83 

71.93 

3.14 

71.92 

3.45 

72 

73 

72.96 

2.55 

72.94 

2.87 

72.93 

3.18 

72.92 

3.50 

73 

74 

73.95 

2.58 

73.94 

2.91 

73.93 

3.23 

7.3.91 

3.55 

74 

75 

74.95 

2.62 

74.94 

2.94 

74.93 

3.27 

74.91 

3.60 

75 

76 

75.95 

2.65 

75.94 

2.98 

75.93 

3.31 

75.91 

3.65 

76 

77 

76.95 

2.69 

76.94 

3.02 

76.93 

3.36 

76.91 

3.70 

77 

78 

77.95 

2.72 

77.94 

3.06 

77.93 

3.40 

77.91 

3.74 

78 

79 

78.95 

2.76 

78.94 

3.10 

78.92 

3.45 

78.91 

3.79 

79 

80 

79.95 

2.79 

79.94 

3.14 

79.92 

3.49 

79.91 

3.84 

80 

81 

80.95 

2.83 

80.94 

3.18 

80.92 

3.53 

80.91 

3.89 

81 

82 

81.95 

2.86 

81.94 

3.22 

81.92 

3.58 

81.91 

3.93 

82 

83 

82.95 

2.90 

82.94 

3.26 

82.92 

3.62 

82.90 

3.98 

83 

84 

83.95 

2.93 

83.94 

3.30 

83.92 

3.66 

83.90 

4.03 

84 

85 

84.95 

2.97 

84.93 

3.34 

84.92 

3.71 

84.90 

4.08 

85 

86 

85.95 

3.00 

85.93 

3.38 

85.92 

3.75 

8s 9“ 

4.13 

86 

87 

86.95 

3.04 

86.93 

3.42 

86.92 

S.79 

86.90 

4.17 

87 

88 

87.95 

3.07 

87.93 

3.45 

87.92 

3.84 

87.90 

4.22 

88 

89 

88.95 

3.11 

88.93 

3.49 

88.92 

3.88 

88.90 

4.27 

89 

90 

89.95 

3.14 

89.93 

3.53 

89.91 

3.93 

89.90 

4.32 

90 

91 

90.95 

3.18 

90.93 

3.57 

90.91 

3.97 

90.90 

4.37 

91 

92 

91.94 

3.21 

91.93 

3.61 

91.91 

4.01 

91.89 

4.41 

92 

93 

92.94 

3.25 

92.93 

3.65 

92.91 

4.06 

92.89 

4.46 

93 

94 

93.94 

3.28 

93.93 

3.69 

93.91 

4.10 

93.89 

4.51 

94 

S5 

94.94 

3.32 

94.93 

3.73 

94.91 

4.14 

94.89 

4.56 

95 I 

96 

95.94 

3 35 

95.93 

3.77 

95.91 

4.19 

95.89 

4.61 

96 

97 

96.94 

3.39 

96.93 

3.81 

96.91 

4.23 

96.89 

4.65 

97 

98 

97.94 

3.42 

97.92 

3.85 

97.91 

4.27 

97.89 

4.79 

98 

99 

98.94 

3.46 

98.92 

3.89 

98.91 

4.32 

98.89 

4.75 

99 

100 

99.94 

3.49 

99.92 

3.93 

99.91 

4.36 

99.88 

4.80 

100 

d 

« 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

o J 

C 

gJ 

00 

O 

83 Deg. 

87| Deg. 

874 Deg. 

87 i Deg. 

cd 

•4-4 

cn 

• H 

Q 
















































































































8 


TRAVERSE TABLE. 


c 

y/ 

r-*- 

3 Deg. 

l 

3} Deg. 

) 

3£ Deg. 

3f Deg. 

a 

Si" 

r* 

P 

3 

O 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

—d 

*-* 

O 

a 

~T 

1.00 

0, 

05 

1 1.00 

0.00 

1.00 

o 

.00 

1.00 

0. 

06 

1 

Ad 

2.00 

0. 

10 

2.00 

0.11 

2.00 

0 

12 

2.00 

0 

13 

2 

3 

3.00 

0. 

16 

3.00 

0.17 

2.99 

0. 

18 

2.99 

9. 

^o 

3 

4 

3.99 

0. 

21 

3.99 

0.23 

3.99 

0. 

24 

3.99 

0. 

26 

1 

fi 

4.99 

0. 

26 

* 4.99 

0.28 

4.99 

0. 

31 

4.99 

0. 

33 

3 

6 

5.99 

0. 

31 

5.99 

0.34 

5.99 

0. 

37 

5.99 

0. 

39 

t> 

7 

6.99 

0. 

37 

6.99 

0.40 

6.99 

0. 

43 

G. 99 

0. 

16 

r* 

( 

8 

7.99 

0. 

42 

7.99 

0.45 

7.99 

0. 

49 

7.98 

0. 

52 

8 

9 

8.99 

0. 

47 

8.99 

0.51 

8.98 

0. 

55 

8.98 

0. 

59 

9 

10 

9.99 

0. 

52 

9.98 

0.57 

9.98 

0. 

61 

9 .98 

0. 

65 

10 

11 

10.98 

0. 

58 

10.98 

0.02 

10.98 

0. 

07 

10.98 

0. 

72 

11 

12 

11.98 

0. 

63 

11.98 

0.68 

11.98 

0. 

73 

11.97 

0. 

78 

12 

13 

12.98 

0. 

63 

12.98 

0.73 

12.98 

0. 

79 

12.97 

0. 

85 

13 

14 

13.98 

0. 

73 

13.98 

0.79 

13.97 

0. 

85 

13.97 

0. 

92 

14 

15 

14.98 

0. 

79 

14.98 

0.85 

14.97 

0. 

92 

14.97 

0. 

98 

15 

16 

15.98 

0. 

84 

15.97 

0.91 

15.97 

0. 

98 

15.97 

1. 

05 

16 

1? 

16.98 

0. 

89 

16.97 

0.96 

16.97 

1. 

04 

16.90 

1. 

11 

17 

18 

17.98 

0. 

94 

17.97 

1 .02 

17.97' 

1. 

10 

17.96 

1. 

18 

18 

19 

18.98 

0. 

99 

18.97 

1.08 

18.96 

1 . 

10 

18.90 

1. 

24 

19 

20 

19.97 

1 . 

05 

19.97 

1.13 

19.90 

1 . 

22 

19.90 

1. 

31 

20 

21 

20.97 

1 . 

10 1 

20.97 

1.19 

20.96 

1 . 

28 

20.96 

1 . 

37 

21 

o-2 
<*- •** 

21.97 

1. 

15 ! 

21 .96 

1.25 

21.96 

1. 

34 

21.95 

1. 

44 

22 

23 

22.97 

1. 

20 

22.96 

1.30 

22.9G 

1. 

40 

22.95 

1. 

50 

23 

24 

23.97 

1. 

26 

23.90 

1.36 

23.96 

1. 

47 

23.95 

1. 

57 

24 

25 

24.97 

1. 

31 

24.90 

1.42 

24.95 

1. 

53 

24.95 

1. 

64 

25 

26 

25.96 

1. 

36 

25.90 

1.47 

25.95 

1. 

59 

25.94 

1. 

70 

26 

27 

26.96 

1. 

41 

26.96 

1.53 

20.95 

1. 

05 

26.94 

1. 

77 

27 

28 

27.96 

1. 

47 

27.95 

1.59 

27.95 

1. 

71 

27.94 

1. 

83 

28 

29 

28.90 

1. 

52 

28.95 

1.64 

28.95 

1. 

77 

28.94 

1 

X • 

90 

29 

30 

29.90 

1. 

57 

29.95 

1.70 

29.94 

1. 

S3 | 

29.94 

1. 

90 

30 

31 

30.96 

1. 

62 

30.95 

1.76 

30.94 

1. 

89 

30.93 

2. 

03 

31 

32 

31.96 

1. 

67 

31.95 

1.81 

31.94 

1. 

95 

31.93 

o 

Ad • 

09 

32 

33 

32.95 

1. 

73 

32.95 

1.87 

32.94 

o 

M • 

01 

32.93 

2. 

16 

33 

34 

33.95 

1. 

78 

33.95 

1.93 

33.94 

2. 

08 

33.93 

2. 

22 

34 

35 

34.95 

1. 

83 

34.94 

1.98 

34.93 

2. 

11 

34.92 

O 

Ad • 

29 

35 

36 

35.95 

1. 

88 

35.94 

2.04 

35.93 

o 

M • 

20 

35.92 

o 

/d • 

35 

36 

37 

36.95 

1. 

94 

30.94 

2.10 

36.93 

o 

Ad • 

20 

36.92 

o 

Ad • 

42 

37 

38 

37.95 

1. 

99 

37.94 

2.15 

37.93 

2. 

32 

37.92 

2. 

49 

38 

39 

38.95 

2. 

04 

38.94 

2.21 

38.93 

o 

Ad • 

38 

38.92 

2. 

55 

39 

40 

39.95 

2. 

09 

39.94 

2.27 

39.93 

o 

44 

39.91 

2. 

62 

40 

41 

40.94 

2. 

15 

40.93 

2.32 

40.92 

"2. 

50 

40.91 

2. 

68 

41 

42 

41.94 

2. 

20 

41.93 

2.38 

41.92 

*) 

Ad • 

56 

41.91 

o 

*-d • 

75 

42 

43 

42.94 

2. 

25 

42.93 

2.44 

42.92 

o 

63 

42.91 

2. 

81 

43 

44 

43.94 

O 

30 

43.93 

2.49 

43.92 

2. 

69 

43.91 

2. 

88 

44 

45 

44.94 

2. 

36 

44.93 

2.55 

44.92 

2. 

75 

44.90 

f> 

dd • 

94 

45 

46 

45.94 

2. 

41 

45.93 

2.61 

45.91 

2. 

81 

45.90 

3. 

01 

4G 

47 

46.94 

2. 

46 

{46.92 

2.66 

46.91 

2. 

87 

46.90 

3. 

07 

4? 

48 

47.93 

O 
<v • 

51 

47.92 

2.72 

47.91 

«> 

d-d • 

93 

47.90 

3. 

14 

48 

49 

48 . 93 

2 # 

56 

48.92 

2.78 

48,91 

2- 

99 

48.90 

3. 

20 

19 

50 

49.93 

2 . 

62 

49.92 

2.83 

49.91 

3. 

05 

49.89 

3. 

27 

50 

o 

o 

G 

Dcp. 

Lilt* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

Z) 

O 

G 

ri 

2 

Q 

87 Deg. 

86} Deg. 

861 

Deg 


86} Dtg 

I 

a 

rt 

Ti 

3 

i 



























































































TRAVERSE TABLE 


& 


5 

a 

P 

3 Deg. 

3} Deg. 

3s Deg. 

C| Deg. 

o 

• 

a o 

pi 

p 

n 

<B 

L?.t. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

CD 

51 

| 50 

.93 

2 

.67 

I 50 

.92 

2.89 

1 50 

.90 

3*11 

50.89 

3.34 

5l 

52 

51 

.93 

O 

A* 

.72 

51 

.92 

2.95 

51 

.90 

3.17 

51.89 

3.40 

52 

5S 

1 52 

.93 

2 

.77 

52 

.91 

3.00 

52 

.90 

3.24 

52.89 

3.47 

53 

54 

53 

.93 

2 

.83 

53 

.91 

3.06 

53 

.90 

3.30 

53.88 

3.53 

54 

55 

! 54 

.92 

2 

.88 

54 

.91 

3.12 

54 

.90 

3.36 

54.88 

3.60 

55 

56 

55 

.92 

o 

A 

.93 

55 

.91 

3.17 

55 

.90 

3.42 

55.88 

3.66 

56 

57 

56 

.92 

2 

.98 

56 

.81 

3.23 

56 

.89 

3.48 

56.88 

3 73 

57 

58 

57 

.92 

3 

.04 

57 

.91 

3.29 

57 

.89 

3.54 

57.88 

3.79 

58 

59 

58 

.92 

3 

.09 

58 

.91 

3.34 

58 

.89 

3.60 

58.87 

3.86 

50 

60 

59 

.92 

3 

14 

59 

.90 

3.40 

59 

.89 

3.66 

59.87 

3.92 

60 

61 

60 

.92 

3 

.19 

60 

.90 

3.46 

1 60 

.89 

3.72 

60.87 

3.99 

61 

62 

61 

.92 

3 

.24 

61 

.90 

3.51 

1 61 

.88 

3.79 

61.87 

4.05 

62 

63 

62 

.91 

3 

.30 

62 

.90 

3.57 

I 62 

.88 

3.85 

62.87 

4.12 

63 

64 

63 

.91 

3 

.35 

63 

.90 

3.63 

63 

.88 

3.91 

63.86 

4.19 

64 

65 

64 

.91 

3 

.40 

64 

.90 

3.69 

64 

.88 

3.97 

64.86 

4.25 

65 

66 

65 

.91 

3 

.45 

65 

.89 

3.74 

65 

.88 

4.03 

65.86 

4.32 

66 

or 

66 

.91 

3 

.51 

66 

.89 

3.80 

66 

.88 

4-09 

66.86 

4.38 

67 

68 

67 

.91 

3 

.56 

67 

.89 

3.86 

67 

.87 

4.15 

67.85 

4.45 

68 

69 

68 

.91 

3 

.61 

68 

.89 

3.91 

68 

.87 

4.21 

68.85 

4.51 

69 

70 

69 

.90 

3 

.66 

69 

89 

3.97 

69 

.87 

4.27 

69.85 

4.58 

70 

71 

70 

.90 

3 

72 

70 

89 

4.03 

70 

.87 

4.33 

70.85 

4.64 

71 

72 

71 

.90 

3 

77 

71 

88 

4.08 

71 

.87 

4.40 

71.85 

4.71 

72 

73 

72 

.90 

3 

82 

72 

8S 

4.14 

72 

.86 

4.46 

72.84 

4.77 

73 

74 

73 

90 

3 

87 | 

73 

88 

4.20 

73 

.86 

4.52 

73.84 

4.84 

74 

75 

74 

90 

3 

93 ! 

74 

88 

4.25 

74 

.86 

4.58 

74.84 

4.91 

75 

76 

75 

.90 

3. 

98 j 

75 

88 

4.31 

75 

86 

4.64 

75.84 

4.97 

76 

77 

76 

89 

4. 

03 

76 

88 

4.37 

76 

86 

4.70 

j76.84 

5.04 

77 

78 

77 

89 

4. 

08 

77 

87 

4.42 

77 

85 

4.76 

77.83 

5.10 

78 

79 

78 

89 

4. 

13 

78 

87 

4.48 

78 

85 

4.82 

!78.83 

5.17 

79 

80 

79 

89 

4. 

19 

79 

87 

4.54 

79 

85 

4.88 

|79.83 

5.23 

80 

81 

80 

89 

4. 

24 

80. 

87 

4.59 

80 

85 

4.94 

80.83 

5.30 

81 

82 

81. 

89 

4. 

29 

81. 

87 

4.65 

81 

85 

5.01 

81.82 

5.36 

82 

83 

82. 

89 

4. 

34 

82. 

87 

4.71 

82 

85 

5.07 

82.82 

5„43 

83 

84 

83. 

88 

4. 

40 

83. 

86 

4.76 

83 

84 

5.13 

83.82 

5.49 

84 

85 

84. 

88 

4. 

45 

84. 

86 

4.82 

84 

84 

5.19 

84.82 

5.56 

85 

86 

85. 

88 

4. 

50 

85. 

86 

4.88 

85 

84 

5.25 

85.82 

5.62 

86 

87 

86. 

88 

4. 

55 

86. 

86 

4.93 

86. 

84 

5.31 

86.81 

5.69 

87 

88 

87 

88 

4. 

61 

87. 

86 

4.99 

87 

84 

5.37 

87.81 

5.76 

88 

89 

88. 

88 

4. 

66 

88. 

86 

5.05 

88. 

83 

5.43 

88.81 

5.82 

89 

90 

89. 

88 

4. 

71 

89. 

86 

5.10 

89. 

83 

5.49 

89.81 

5.89 

90 

91 

90. 

88 

4. 

76 

90. 

85 

5.16 

90. 

83 

5.56 

90.81 

5.95 

9i 

92 

91 . 

87 

4. 

81 

91. 

85 

5.22 

91. 

83 

5.62 

91.80 

6.02 

92 

93 

92. 

87 

4. 

87 

92. 

85 

5.27 

92. 

83 

5.68 

92.80 

6.08 

93 

94 

93. 

87 

4. 

92 

93. 

85 

5.33 

93. 

82 

5.74 

93.80 

6.15 

94 

95 

94. 

87 

4. 

97 

94. 

85 

5.39 

94. 

82 

5.80 

94.80 

6.21 

95 

96 

95. 

87 

5. 

02 

95. 

85 

5.4 1 

95. 

82 

5.86 

95.79 

6.28 

96 

97 

96. 

87 

5. 

08 

96. 

84 

5 :o 

96. 

82 

5.92 

96.79 

0.34 

97 

98 1 

97. 

87 

5. 

13 

97. 

84 

5.56 

97. 

82 

5.98 

97.79 

6.41 

98 

99 

98. 

86 

5. 

18 

98. 

84 

5.61 

98. 

82 

6.04 

93.79 

6.47 

99 

100 

99. 

86 

5. 

23 

99. 

84 

5.67 

99. 

81 

6.10 

99.79 

6.54 

100 

d 

G 

a 

Dcp. 

Lat. 

Der>. 

A 

Lai. 

Dep. 

Lat. 

Dop. 

X ja t. 

C 

c 

a 

ci 

o 

87 Dog. 

| 

86i Deg. 

83'- Deg. 

86} Deg. 

• H 

a 






























































































10 


TRAVERSE TABLE 


Distance.J 

4 Deg. 

4i Deg. 

4-2 Deg. 

4J Deg. 

Distance.! 

1 

Ijdt* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

X 

Lat. 

Dep. 

1 

1.00 

0.07 

1.00 

0.0? 

1.00 

0.08 

1.00 

0.08 

1 

2 

2.00 

0.14 

1.99 

0.15 

1.99 

0 16 

1.99 

0.17 

% l 

3 

2.99 

0.21 

2.99 

0.22 

2.99 

0 24 

2.99 

0.25 

3 

4 

a 99 

0.28 

3.99 

0.30 

3.99 

0 31 

3.98 

0.33 

1 ‘ 

5 

4. 99 

0.35 

4.99 

0.37 

4.98 

0.39 

4.98 

0.41 

5 

6 

5.99 

0.42 

5.98 

0.44 

5.98 

0.47 

5.98 

0.50 

6 

7 

6.98 

0.49 

6.98 

0.52 

6.98 

0.55 

6.97 

0.58 

7 

8 

7.98 

0.56 

7.98 

0.59 

7.98 

0.63 

7.97 

0.66 

8 

9 

8.98 

0.63 

8.98 

0.67 

8.97 

0.71 

8.97 

0.75 

9 

10 

9.98 

0.70 

9.97 

0.74 

9.97 

0.78 

9.97 

0.83 

10 

11 

10.97 

0.77 

10.97 

0.82 

10.97 

0.86 

10.96 

0.91 

11 

12 

11.97 

0.84 

11.97 

0.89 

11.96 

0.94 

11.96 

0.99 

12 

13 

12.97 

0.91 

12.96 

0.96 

12.96 

1.02 

12.96 

1.08 

J 3 

14 

13.97 

0.98 

13.96 

1.04 

13.96 

1.10 

13.95 

1.16 

14 

15 

14.96 

1.05 

14.96 

1.11 

14.95 

1.18 

14.95 

1.24 

15 

16 

15.96 

1.12 

15.96 

1.19 

15.95 

1.26 

15.95 

1.32 

16 

17 

16.96 

1.19 

16.95 

1.26 

16.95 

1.33 

16.94 

1.41 

17 

18 

17.96 

1.26 

17.95 

1.33 

17.94 

1.41 

17.94 

1.49 

18 

19 

18.95 

1.33 

18.95 

1.40 

18.94 

1.49 

18.93 

1.57 

19 

20 

19.95| 

1.40 

19.95 

1.48 

19.94 

1.57 

19.93 

1.66 

20 

21 

20.95 

1.46 

20.94 

1.56 

20.94 

1.65 

20.93 

1.74 

21 

22 

21.95 

1.53 

21.94 

1.63 

21.93 

1.73 

21.92 

1.82 

22 

23 

22.94 

1.60 

22.94 

1.70 

22.93 

1.80 

22.92 

1.90 

23 

24 

23.94 

1.67 1 

23.93 

1.78 

23.93 

1.88 

23.92 

1.99 

24 

25 

24.94 

1.74 

24.93 

1.85 

24.92 

1.96 

24.91 

2.07 

25 

26 

25.94 

1.81 

125.93 

1.93 

25.92 

2.04 

25.91 

2.15 

26 

27 

26.93 

1.88 

26.93 

2.00 

26.92 

2.12 

26.91 

2.24 

27 

28 

27.93 

1.95 

27.92 

2.08 

27.91 

2.20 

27.90 

2.32 

28 

29 

28.93 

2.02 

28.92 

2.15 

28.91 

2.28 

28.90 

2.40 

29 

30 

29.93 

2.09 

29.92 

2.22 

29.91 

2.35 

29.90 

2.48 

30 

31 

30.92 

2.16 

30.91 

2.30 

30.90 

2.43 

30.89 

2.57 

31 

32 

31.92 

2.23 

31.91 

2.37 

31.90 

2.51 

31.89 

2.65 

32 

33 

32.92 

2.30 

32.91 

2.45 

32.90 

2.59 

32.89 

2.73 

33 

34 

33.92 

2.37 

33.91 

2.52 

33.90 

2.67 

33.88 

2.82 

34 

35 

34.91 

2.44 

34.90 

2.59 

34.89 

2.75 

34.88 

2.90 

35 

36 

35.91 

2.51 

35.90 

2.67 

35.89 

2.82 

35.88 

2.98 

36 

37 

36.91 

2.58 

36.90 

2.74 

36.89 

2.90 

36.87 

3.06 

37 

33 

37.91 

2.65 

37.90 

2.82 

37.88 

2.98 

37.87 

3.15 

38 

39 

38.90 

2.72 

38.89 

2.89 

38.88 

3.06 

38.87 

3.23 

39 

40 

39.90 

2.79 

39.89 

2.96 

39.88 

3.14 

39.86 

3.31 

40 

41 

40.90 

2.86 

40.89 

3.04 

40.87 

3.22 

40.86 

3.40 

"41 

42 

41.90 

2.93 

41.88 

3.11 

41.87 

3.30 

41.86 

3.48 

42 

43 

42.90 

3.00 

42.88 

3.19 

42.87 

3.37 

42.85 

3.56 

43 

44 

43.89 

3.07 

43.88 

3.26 

43.86 

3.45 

43.85 

3.64 

44 

45 

44.89 

3.14 

44.88 

3.33 

44.86 

3.53 

44.85 

3.73 

45 

46 

45.89 

3.21 

45.87 

3.41 

45.86 

3.61 

45.84 

3.81 

46 

47 

46.89 

3.28 

46.87 

3.48 

46.86 

3.69 

46.84 

3.89 

4 ? 

48 

47.88 

3.35 

47.87 

3.56 

47.85 

3.77 

47.84 

3.97 

49 

49 

48.88 

3.42 

48.87 

3.63 

48.85 

3.84 

48.83 

4.06 

49 

60 

49.88 

3.49 

49.86 

3.71 

49.85 

3.92 

49.83 

4.14 

50 

8 

C 

cd 

£ 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance.! 

| 86 Deg. 

85J Deg. 

85| Deg. 

85J Deg. 



























































































































TRAVERSE TABLE. 


n 


o 

CO 

r-*- 

P 

i 

4 Dog. 

4i Deg. 

4£ Deg. 

4| Deg. 

O 

5a 

3 

o 

(5 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

c: 

51 

50.88 

3.56 

50.86 

3.78 

50.84 

4.00 

50.82 

4.22 

51 

52 

51.87 

3.63 

51.86 

3.85 

51.84 

4.08 

51.82 

4.31 

52 

53 

52.87 

3.70 

52.85 

3.93 

52.84 

4.16 

52.82 

4.39 

53 

64 

53.87 

3.77 

53.85 

4.00 

53.83 

4.24 

53.81 

4.47 

54 

65 

54.87 

3.84 

54.85 

4.08 

54.83 

4.32 

54.81 

4-55 

55 

66 

55.86 

3.91 

55.85 

4.15 

55.83 

4.39 

55.81 

4.64 

56 

67 

56.86 

3.98 

56.84 

4.22 

56.82 

4.47 

56.80 

4.72 

57 

68 

57.86 

4.05 

57.84 

4.30 

57.82 

4.55 

57 80 

4.80 

58 

59 

58.86 

4.12 

58.84 

4.37 

58.82 

4.63 

58.80 

4.89 

59 

60 

59.85 

4.19 

59.84 

4.45 

59.82 

4.71 

59.79 

4.97 

60 

l 61 

60.85 

4.26 

60.83 

4.52 

60.81 

4.79 

60.79 

5.05 

61 

62 

61.85 

4.32 

61.83 

4.59 

61.81 

4.86 

61.79 

5.13 

62 

63 

62.85 

4.39 

62.83 

4.67 

62.81 

4.94 

62.78 

5.22 

63 

64 

63.84 

4.46 

63.82 

4.74 

63.80 

5.02 

63.78 

5.30 

64 

65 

64.84 

4.53 

64.82 

4.82 

64.80 

5.10 

64.78 

5.38 

65 

66 

65.84 

4.60 

65.82 

4.89 

65.80 

5.18 

65.77 

5.47 

66 

67 

66.84 

4.67 

66.82 

4.97 

66.79 

5.26 

66.77 

5.55 

67 

68 

67.83 

4.74 

67.81 

5.04 

67.79 

5.34 

67.77 

5.63 

63 

69 

68.83 

4.81 

68.81 

5.11 

68.79 

5.41 

68.76 

5.71 

69 

70 

69.83 

4.88 

69.81 

5.19 

69.78 

5.49 

69.76 

5.80 

70 

71 

70.83 

4.95 

70.80 

5.26 

70.78 

5.57 

70.76 

5.88 

71 

72 

71.82 

5.02 

71.80 

5.34 

71.78 

5.65 

71.75 

5.96 

72 

73 

72.82 

5.09 

72.80 

5.41 

72.77 

5.73 

72.75 

6.04 

73 

74 

73.82 

5.16 

73.80 

5.48 

73.77 

5.81 

73.75 

6.13 

74 

75 

74.82 

5.23 

74.79 

5.56 

74.77 

5.88 

74.74 

6.21 

75 

76 

75.81 

5.30 

75.79 

5.63 

75.77 

5.96 

75.74 

6.29 

76 

77 

76.81 

5.37 

76.79 

5.71 

76.76 

6.04 

76.74 

6.38 

77 

78 

77.81 

5.44 

77.79 

5.78 

77.76 

6.12 

77.73 

6.46 

78 

79 

78.81 

5.51 

78.78 

5.85 

78.76 

6.20 

78.73 

6.54 

79 

80 

79.81 

5.58 

79.78 

5.93 

79.75 

6.28 

79.73 

6.62 

80 

81 

80.80 

5.65 

80.78 

6.00 

80.75 

6.36 

80.72 

6.71 

81 

82 

81.80 

5.72 

81.78 

6.08 

81.75 

6.43 

81.72 

6.79 

82 

83 

82.80 

5.79 

82.77 

6.15 

82.74 

6.51 

82.71 

6.87 

83 

84 

83.80 

5.86 

83.77 

6.23 

83.74 

6.59 

83.71 

6.96 

84 

85 

84.79 

5.93 

84.77 

6.30 

84.74 

6.67 

84.71 

7.04 

85 

86 

85.79 

6.00 

85.76 

6.3? 

85.73 

6.75 

85.70 

7.12 

86 

87 

86.79 

6.07 

86.76 

6.45 

86.73 

6.83 

86.70 

7.20 

87 

88 

87.79 

6.14 

87.76 

6.52 

87.73 

6.90 

87.70 

7.29 

83 

89 

88.78 

6.21 

88.76 

6.60 

83.73 

6.98 

88.70 

7.37 

89 

90 

89.78 

6.28 

89.75 

6.67 

89.72 

7.06 

89.69 

7.45 

90 

91 

90.78 

6.35 

90.75 

6.74 

90.72 

7.14 

90.69 

7.54 

91 

92 

91.78 

6.42 

91.75 

6.82 

91.72 

7.22 

91.68 

7.62 

92 

93 

92.77 

6.49 

92.74 

6.89 

92.71 

7.30 

92.68 

7.70 

93 

94 

93.77 

6.56 

93.74 

6.97 

93.71 

7.38 

93.68 

7.78 

94 

95 

94.77 

6.63 

94.74 

7.04 

94.71 

7.45 

94.67 

7.87 

95 

96 

95.77 

6.70 

95.74 

7.11 

95.70 

7.53 

95.67 

7.95 

96 

, 97 

96.76 

6.77 

96.73 

7.19 

96.70 

7.61 

96.67 

8.03 

97 

1 93 

97.76 

6.84 

97.73 

7.26 

97.70 

7.69 

97.66 

8.12 

98 

99 

98.76 

6.91 

98.73 

7.34 

98.69 

7.77 

98.66 

8.20 

99 

100 

99.76 

6.98 

99.73 

7.41 

99.69 

7.85 

99.66 

8.28 

100 

• 

03 

U 

£3 

Dep. 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

a 

«< 

*\ 

'll 

86 Deg. 

85| Deg, 

85i Deg. 

85 £ Deg. 






























































































TRAVERSE TABLE 


12 


Distance. 

5 Deg. 

5\ Deg. 

5’- Deg. 

5$ Deg. 

Distance.1 
l 

Lat. 

DeD. 

A 

Lat. j 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

I 

1 ,00 

0. 

09 

1.00 

0.09 

1.00 

0.10 

0.99 

0.10 

1 

n 

* 

1 .99 

0. 

17 

1.99 

0.18 

1.99 

0.19 

1.99 

0.20 

2 

3 

2.99 

0. 

26 

2.99 

0.27 

2.99 

0.29 

2.98 

0.80 

3 

4 

3.93 

0. 

35 

3.98 

0.37 

3.98 

0.38 

3.98 

0.40 

4 

5 

4 . 93 

0. 

44 

4.98 

0.46 

4.98 

0.48 

4.97 

0.50 

5 

6 

5.93 

0. 

52 

5.97 

0.55 

5.97 

0.58 

5.97 

0.60 

6 

7 

6.97 

0. 

61 

6.97 

0.64 

6.97 

0.67 

6.96 

0.70 

i 

8 

7.97 

0. 

70 

7.9 7 

0.73 

7.96 

0.76 

7.96 

0.80 

8 

9 

8.97 

0. 

78 1 

8.96 

0.82 

8 96 

0.86 

8.95 

0.90 

9 

10 

9.96 

0. 

87 

9.96 

0.92 

9.95 

0.96 

9.95 

1.00 

10 

11 

10.96 

0. 

96 

10.95 

l .01 

10.95 

1.05 

10.94 

1.10 

11 

12 

11.95 

1 . 

05 

i 1.9o 

1.10 

11.94 

1.15 

11.94 

1.20 

1 ~ 

13 

12.95 

1. 

13 

12.95 

1.19 

12.94 

1.25 

12.93 

1.30 

13 , 

14 

13.95 

1 . 

22 

13.94 

1.28 

13.94 

1.34 

13.93 

1.40 

14 

15 

14.94 

1. 

31 

14.94 

1.37 

14.93 

1.44 

14.92 

1.50 

15 

16 

15.94 

1. 

39 

15.93 

1.46 

15.93 

1.53 

15.92 

1.60 

16 

17 

16.94 

1 . 

48 

16.93 

1.56 

16.92 

1.63 

16.91 

1.70 

17 

13 

17.93 

1 . 

57 

17.92 

1.65 

17.92 

1.73 

17.91 

1.80 

18 

19 

18.93 

1 . 

66 

18.92 

1.74 

18.91 

1.82 

18.90 

1.90 

19 

20 

19.92 

1 . 

74 

19.92 

1.83 

19.91 

1.92 

19.90 

2.00 

20 

21 

20.92 

1 . 

83 

20.91 

1.92 

20.90 

2.01 

20.89 

2.10 

21 

22 

21.92 

1 . 

92 

21.91 

2.91 

21.90 

2.11 

21.89 

2.20 

22 

23 

22.91 

2. 

00 

22.90 

2.10 

22.89 

2.20 1 

22.88 

2.30 

23 

24 

23.91 

2. 

09 

23.90 

2.20 

23.89 

2.30 

23.88 

2.40 

24 

25 

24.90 

2. 

18 

24.90 

2.29 

24.88 

2.40 

24.87 

2.50 

25 

26 

25.90 

2. 

27 

25.89 

2.38 

25.88 

2.49 

25.87 

2.60 

26 

27 

26.90 

2. 

35 

26.89 

2.47 

26.88 

2.59 | 

26.86 

2.71 

27 

23 

27.89 

2. 

44 

27.88 

2.56 

27.87 

2.68 

27.86 

2.81 

28 

29 

23.89 

2. 

5.3 

28.88 

2.65 

28.87 

2.78 

28.85 

2.91 

29 

30 

29.89 

2. 

61 

29.87 

2.75 

29.86 

2.88 

29.85 

3.01 

30 

31 

30.88 

2. 

70 

30.87 

2.84 

30.86 

2.97 

30.84 

3.11 

31 

32 

31.88 

2 

79 

31.87 

2.93 

31.85 

3.07 

31.84 

3.21 

32 

33 

32.87 

2 

88 

32.86 

3.02 

32.85 

3.16 

32.83 

3.31 

33 

34 

33.87 

2 

96 

33.86 

3.11 

33.84 

3.26 

33.83 

3.41 

34 

35 

34.87 

3 

05 

34.85 

3.20 

34.84 

3.35 

34.82 

3.51 

35 

36 

35.86 

3 

14 

35.85 

3.29 

35.83 

3.45 

35.82 

3.61 

36 

37 

30.86 

3 

22 

36.84 

3.39 

36.83 

3.55 

36.81 

3.71 

37 

38 

37.86 

3 

31 

37.84 

3.48 

37.83 

3.64 

37.81 

3,81 

38 

39 

38.85 

3 

40 

38.84 

3.57 

38.82 

3.74 

38.80 

3.91 

39 

40 

39.85 

3 

.49 

39.83 

3.66 

39.82 

3.83 

39.80 

4.01 

| 40 

41 

40.84 

3 

.57 

40.83 

3.75 

40.81 

3.93 

40.79 

4.11 

41 

42 

41.84 

3 

.66 

41.82 

3.84 

41.81 

4.03 

41.79 

4.21 

42 

43 

42.84 

3 

.75 

42.82 

3.93 

42.80 

4.12 

42.78 

4 .31 

43 

44 

43.83 

3 

.83 

43.82 

4.03 

43.80 

4.22 

43.78 

4,41 

44 

45 

44.83 

3 

.92 

44.81 

4.12 

44.79 

4.31 

44.77 

4 51 

45 

46 

45.82 

4 

.01 

45.81 

4.21 

45.79 

4.41 

45.77 

4 61 

46 

47 

46.82 

4 

.10 

46.80 

4.30 

46.78 

4.50 

46.76 

4.71 

47 

43 

47.82 

4 

.18 

47.80 

4.39 

47.78 

4.60 

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49 

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4 

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48,79 

4.48 

48.77 

4.70 

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49.79 

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49.75 

5.01 

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w 

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1 ^ 

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Lat. 

Dep. 

j Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

c 

H 

a 

85 Deg 


84$ Deg. 

' 84^ 

Deg. 

84} Deg. 

1 














































































































TRAVERSE TAHLE. 


13 


o 

00 

p 

3 

o 

a> 

5 Deg. 

5i Deg. 

Deg 


53 Deg. 

C 

Crt’ 

«-* 

d 

O 

CO 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50 

.81 

4.44 

50.79 

4.67 

50.77 

4. 

89 

50 74 

5.11 

51 

52 

51 

.80 

4.53 

51.78 

4.76 

51.76 

4. 

98 

51 74 

5.21 

52, 

53 

52 

.80 

4.62 

52.78 

4.85 

52.76 

5. 

08 

52 73 

5.31 

5:| 

54 

53 

.79 

4.71 

53.77 

4.94 

53.75 

5. 

18 

53 73 

5.41 

5 'f 

55 

51 

.79 

4.79 

54.77 

5.03 

54.75 

5. 

27 

54.72 

5.51 

9.' 

56 

55 

.79 

4.88 

55.77 

5.12 

55.74 

5. 

37 

55.72 

5.61 

561 

S 57 

56 

.78 

4.97 

56.76 

5.22 

56.74 

5. 

46 

56.71 

5.71 

57 

58 

57 

.78 

5.06 

57.76 

5.31 

57.73 

5. 

56 

57.71 

5.81 

58 

59 

58 

.78 

5.14 

58.75 

5.40 

58.73 

5. 

65 

58.70 

5.91 

59 

60 

59 

.77 

5.23 

59.75 

5.49 

59.72 

5. 

75 

59.70 

6.01 

60 

61 

60 

.77 

5.32 

60.74 

5.58 

60.72 

5. 

85 

60.69 

6.11 

61 

62 

61 

.76 

5.40 

61.74 

5.67 

61.71 

5. 

94 

61.69 

6.21 

62 

63 

62 

.76 

5.49 

62.74 

5.76 

62.71 

6. 

04 

62.68 

6.31 

63 

64 

63 

.76 

5.58 

63.73 

5.86 

63.71 

6. 

13 

63.68 

6.41 

64 

65 

64 

.75 

5.67 

64.73 

5.95 

64.70 

6. 

23 

64.67 

6.51 

65 

66 

65 

.75 

5.75 

65.72 

6.04 

65.70 

6. 

33 

65.67 

6.61 

66 

67 

66 

.75 

5.84 

66.72 

6.13 

66.69 

6. 

42 

66.66 

6.71 

6"/ 

68 

67 

.74 

5.93 

67.71 

6.22 

67.69 

6. 

52 

67.66 

6.81 

68 

69 

68 

.74 

6.01 

68.71 

6.31 

68.68 

6. 

61 

68.65 

6.91 

69 

70 

69 

.73 

6.10 

69.71 

6.41 

69.68 

6. 

71 

69.65 

7.01 

70 

71 

70 

.73 

6.19 

70.70 

6.50 

70.67 

6. 

81 

70.64 

7.11 

71 

72 

71 

.73 

6.28 

71.70 

6.59 

71.67 

6. 

90 

71.64 

7.21 

72 

73 

72 

.72 

6.36 

72.69 

6.68 

72.66 

7. 

00 

72.63 

7.31 

73 

74 

73 

.72 

6.45 

73.69 

6.77, 

73.66 

7. 

09 

73.63 

7.41 

74 

75 

74 

.71 

6.54 

74.69 

6.86 

74.65 

7. 

19 

74.62 

7.51 

75 

76 

75 

.71 

6.62 

75.68 

6.95 

75.65 

7. 

28 

75.62 

7.61 

76 

77 

76 

.71 

6.71 

76.68 

7.05 

76.65 

7. 

38 

76.61 

7.71 

77 

78 

77 

.70 

6.80 

77.67 

7.14 

77.64 

7. 

48 

77.61 

7.81 

78 

79 

73 

.70 

6.89 

78.67 

7.23 

78.64 

7. 

57 

78.60 

7.91 

79 

80 

79 

.70 

6.97 

79.66 

7.32 

79.63 

7. 

67 

79.60 

8.02 

80 

81 

80 

.69 

7.06 

80.66 

7.41 

80.63 

7. 

76 

80.59 

8.12 

81 

82 

81 

.69 

7.15 

81.66 

7.50 

81.62 

7. 

86 

81.59 

8.22 

82 

83 

82 

.68 

7.23 

82.65 

7.59 

82.62 

7. 

96 

82.58 

8.32 

83 

84 

83 

.68 

7.32 

83.65 

7.69 

83.61 

8. 

05 

83.58 

8.42 

84 

85 

84 

.68 

7.41 

84.64 

7.78 

84.61 

8. 

15 

84.57 

8.52 

85 

86 

85 

.67 

7.50 

85.64 

7.87 

85.60 

8. 

24 

85.57 

8.62 

86 

87 

86 

.67 

7.5S 

86.64 

7.96 

86. GO 

8. 

34 

86.56 

8.72 

87 

88 

87 

.67 

7.67 

87.63 

8.05 

87.59 

8. 

43 

87.56 

8.82 

88 

89 

88 

. 66 

7.76 

88.63 

8.14 

88.59 

8. 

53 

88.55 

8.92 

89 

90 

89 

.66 

7.84 

89.62 

8.24 

89.59 

8. 

63 

89.55 

9.02 

90 

91 

90 

.65 

7.93 

90.62 

8.33 

90.58 

8. 

72 

90.54 

9.12 

91 

92 

91 

.65 

8.02 

91.61 

8.42 

91.58 

8. 

82 

91.54 

9.22 

92 

93 

92 

.65 

8.11 

92.61 

8.51 

92.57 

8. 

91 

92.53 

9.32 

93 

94 

93 

.64 

8.19 

93.61 

8.60 

93.57 

9. 

01 

93.53 

9.42 

94 

95 

94 

.64 

8.28 

94.60 

8.69 

94.56 

9. 

11 

94.52 

9.52 

95 

96 

95 

.63 

8.37 

95.60 

8.78 

95.56 

9. 

20 

95.52 

9.62 

96 

97 

96 

.63 

8.45 

96.59 

8.88 

96.55 

9. 

30 

96.51 

9.72 

97 

98 

97 

.63 

8.54 

97.59 

8.97 

97.55 

9. 

39 

97.51 

9.82 

98 

99 

98 

.62 

8 63 

98.59 

9.06 

98.54 

9. 

49 

98.50 

9.92 

99 

100 

99 

.62 

8.72 

99.58 

9.15 

99.54 

9. 

58 

99.50 

10.02 

100 

Distance.| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

<S> 

o 

d 

d 

*-» 

co 

•H 

£j 

85 Deg. 

84$ Deg. 

i 

84i Deg 

• 

84J Deg 


20 































































































14 


TRAV7RSE TAliLE. 


Distance. 

1 

6 Deg. 

Deg. 

Deg. 

6? Deg. 

| Distanced 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dtp. 

Lat. 

Dep. 

i j 

0,99 

0.10 

9.99 

0. 

11 

0.99 

0. 

11 

0.99 

0.12 

1 


1 99 

0.21 

1.99 

0. 

22 

1.99 

0. 

23 

1.99 

0 24 

2 

\ 3 

2 98 

0.31 

2.98 

0. 

33 

2.98 

0. 

34 

2.98 

0 35 

3 

4 ' 

3 98 

0.41 

3.98 

0 

44 

3.97 

0. 

45 

3.97 

0.47 

4 

6 

4.97 

0.52 

4.97 

0 . 

54 

4.97 

0. 

57 

4.97 

0.59 

5 

6 

5.97 

0.63 

5.96 

0. 

65 

5.96 

0. 

6S 

5.96 

0.71 

8 

7 

6.96 

0.73 

6.96 

0. 

76 

6.96 | 

0. 

79 

6.95 

0.82 

7 

8 

7.96 

0.84 

7.95 

0. 

87 

7.95 

0. 

91 

7.94 

0.94 

9 

9 

8.95 

0.94 

8.95 

0. 

98 

8.94 

1. 

02 

8.94 

1.0G 

9 

10 

9.95 

1.05 

9.94 

1 . 

09 

9.94 

1 . 

13 

9.93 

1.18 

10 

11 

10.94 

1.15 

10.93" 

1. 

20 

10.93 

1 . 

25 

10.92 

1.29 

11 

12 

11.93 

1 .25 

11.93 

1 . 

31 

11.92 

1 . 

36 

11.92 

1.41 

12 

13 

12.93 

1.36 

12.92 

1. 

42 

12.92 

1 . 

47 

12.91 

1.53 

13 

14 

13.92 

1.46 

13.92 

1 . 

52 

13.91 

1 . 

59 

13.90 

1.65 

14 

15 

14.92 

1.57 

14.91 

1 . 

63 

14.90 

1 . 

70 

14.90 

1.76 

15 

16 

15.91 

1.67 

15.90 

1. 

74 

15.90 

1 . 

81 

15.89 

1.88 

16 

17 

16.91 

1.78 

16.90 

1. 

85 

16.89 

1 . 

92 

16.88 

2 00 

17 

18 

17.90 

1.88 

17.89 

1 . 

96 

17.88 

2. 

04 

17.88 

2.12 

18 

19 

18.90 

1.99 

18.89 

o 

** 

07 

18.88 

2. 

15 

18.87 

2.23 

19 

20 

19.89 

2.09 

19.83 

2. 

18 

19.87 

2. 

26 

19.86 

2.35 

20 

21 

20.88 

2.20 

20.88 

2. 

29 

20.87 

2. 

38 

20.85 

2.47 

21 

22 

21.88 

2.30 

21.87 

2. 

40 

21.86 

2. 

49 

21.85 

2.59 

22 

23 

22.87 

2.40 

22.86 

2. 

50 

22.85 

2. 

60 

22.84 

2.70 

23 

24 

23.S7 

2.51 

23.86 

2 

61 

23.85 

2. 

72 

23.83 

2.82 

24 

25 

24.86 

2.61 

24.85 

2 

72 

24.84 

2 

83 

24.83 

2.94 

25 

26 

25.86 

2.72 

25.85 

2 

83 

25.83 

2. 

94 

25.82 

3.06 

26 

27 

26.85 

2.82 

26.84 

2 

94 

26.83 

3 

06 

26.81 

3.17 

27 

28 

27.85 

2.93 

27.83 

3 

05 

27.82 

3 

17 

27.81 

3.29 

28 

29 

28.84 

3.03 

28.83 

3 

16 

28.81 

3 

28 

28.80 

3.41 

29 

30 

29.84 

3.14 

29.82 

3 

.27 

29.81 

3 

40 

29.79 

3.53 

30 

31 

30.83 

3.24" 

30.82 

3 

37 

30.80 

3 

51 

30.79 

3.64 

31 

32 

31 82 

3.34 

31.81 

3 

.48 

31.79 

3 

62 

31.78 

3.76 

32 

33 

32.82 

3.45 

32.80 

3 

.59 

32.79 

3 

74 

32.77 

3.88 

33 

34 

33.81 

3.55 

33-30 

3 

.70 

33.78 

3 

85 

33.76 

4.00 

34 

35 

34.81 

3.66 

34.79 

3 

.81 

34.78 

3 

.96 

34.76 

4.11 

35 

36 

35.80 

3.76 

35.79 

3 

.92 

35.77 

4 

.08 

35.75 

4.23 

36 

37 

36.80 

3.87 

36.78 

4 

.03 

36.76 

4 

.19 

36.75 

4.35 

37 

38 

37.79 

3.97 

37.77 

4 

.14 

37.76 

4 

.30 

37.74 

4.47 

33 

39 

38.79 

4.08 

38.77 

4 

.25 

38.75 

4 

.41 

38.73 

4.58 

39 

40 

39.78 

4.18 

39.76 

4 

.35 

39.74 

4 

.53 

39.72 

4.70 

40 

41 

40.78 

4.29 

40.76 

4 

46 

40.74 

4 

.64 

40.72 

4.82 

41 

42 

41.77 

4.39 

41.75 

4 

.57 

41.73 

4 

.76 

41.71 

4.94 

42 

43 

42.76 

4.49 

42.74 

4 

.68 

42.72 

4 

.87 

42.70 

5.05 

43 

44 

43.76 

4.60 

43.74 

4 

.79 

43.72 

4 

.98 

43.70 

5.17 

44 

45 

44.75 

4.70 

44.73 

4 

.90 

44.71 

5 

.09 

44.69 

5.29 

45 

46 

45.75 

4.81 

45.73 

5 

.01 

45.70 

5 

.21 

45.68 

5.41 

i 46 

47 

46.74 

4.91 

46.72 

5 

.12 

46.70 

5 

.32 

46.67 

5 52 

4? 

48 

47.74 

5.02 

47.71 

5 

.23 

47.69 

5 

.43 

47.67 

5. 64 

48 

49 

48.73 

5.12 

48.71 

5 

.34 

48.69 

5 

.55 

48.66 

5. 76 

19 

60 

49.73 

5.23 

49.70 

5 

.44 

49.68 

5 

.66 

49.65 

5.88 

50 

© 

S 

a 

3 

a 

Q 

mmm 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

r . 

! V 

O 

84 Deg. 

83f Deg. 

' 83 1 

i 

Deg. 

83J Deg. 

& 













































































































TRAVERSE TABLE. 


15 


o 

j ® 

r+ 

V 

6 Deg. 

■ i 

6} Deg. 

6i Deg 

61 Deg. 

Distance. 

i ~ 

! a 

o 

Lrt. 

Dep. 

Lat. 

Dep. 

J at. | 

Dep. j 

1 

Lat. 

D“p. 

54 

50.72 

5.S3 

50.70 

' 5.55 

50.67 

5.7* j 

56.65 

5,99 

51 

52 

51.72 

5.44 

51.69 

5.66 

51.67 

5.89 | 

51.64 

6.11 

52 

< 53 

52.71 

5.54 

52.68 

5.77 

52.66 

6 09 1 

52.63 

6.2? 

53 

54 

53.70 

5.64 

53.68 

5.88 

53.65 

6.1 1 . 

53.63 

6.35 

54 

55 

54.70 

5.75 

54.67 

5.99 

54.65 

6*23 

54.62 

6.16 

55 

66 
* 57 

55.69 

5.85 

55.67 

6.10 

55.64 

6 34 

55.61 

6.58 

56 

56.69 

5.96 

56.66 

6.21 

56.63 

6.45 

56.60 

6.70 

57 

68 

57.68 

6. 06 

57.66 

6.31 

57.63 

6-57 

57.60 

6.82 

58 

58 

58.68 

6.1/ 

58.65 

6.42 

58.62 

5.68 

58.59 

6.93 

59 

{ 66 

59.67 

6.27 

59.64 

6.53 

59.61 

6-79 

59.58 

7.05 

60 

j 61 

60.67 

6.38 

60.64 

6.64 

60.61 

6.91 

60.58 

7.17 

61 

I 62 

61.66 

6.48 

61.63 

6.75 

61.60 

7.02 

61.57 

7.29 

62 

j 63 

62.65 

6.59 

62.63 

6.86 

62.60 

7.13 

62.56 

7.40 

63 

; 64 

63.65 

6.69 

63.62 

6.97 

63.59 

7.25 

63.56 

7.52 

64 

I 65 

64.64 

6.79 

64.61 

7.08 

64.58 

7.36 

64.55 

7.64 

65 

: 66 

65.64 

6.90 

65.61 

7 19 

€5.58 

7.47 

65.54 

7.76 

66 

i 67 

66.63 

7.00 

66.60 

7.29 

66.57 

7 58 

66.54 

7.88 

67 

: 68 

67.63 

7.11 

67.60 

7.40 

67.56 

7.70 

67.53 

7.99 

68 

; 69 

68.62 

7.21 

68,59 

7.51 

68.56 

7.81 

68.52 

8.11 

69 

i 70 

69.62 

7.32 

69.58 

7.62 

69.55 

7.92 

69.51 

8.23 

70 

71 

70. Gl 

7.42 

70.58 

7.73 

70.54 

8.04 

70.51 

8.35 

71 

i 72 

71.61 

7.53 

71.57 

7.84 

71.54 

8.15 

71.50 

8.46 

72 

; 73 

72.60 

7.63 

72.57 

7.95 

72.53 

8.26 

72.49 

8.58 

73 

l 74 

73.59 

7.74 

73.56 

8.06 

73.52 

8.38 

73.49 

8.70 

74 

75 

74.59 

7.84 

74.55 

8.17 

74.52 

8.49 

174.48 

8.82 

75 

j 76 

75.58 

7.94 

75.55 

8.27 

75.51 

8.60 

,75.47 

8.93 

76 

; 77 

76.58 

8.05 

76.54 

8.38 

76.51 

8,72 

76.47 

9.05 

77- 

; 78 

77.57 

8.15 

77.54 

8.49 

77.50 

8.83 

77.46 

9.17 

78 

i 79 

78.57 

8.26 

78.53 

8.60 

78.49 

8.94 

78.45 

9.29 

79 

; so 

79.56 

8.36 

79.53 

8.71 

79.49 

9.06 

79.45 

9.40 

80 

< 81 

80.56 

8.47 

80.52 

8.82 

80.48 

9.17 

80.44 

9.52 

81 

: 82 

81.55 

8.57 

81.51 

8.93 

81.47 

9.28 

81.43 

9.64 

82 

j 83 

82.55 

8.68 

82.51 

9.04 

82.47 

9.40 

82.42 

9.76 

83 

84 

83.54 

8.78 

83.50 

9.14 

83-46 

9.51 

83.42 

9.87 

84 

1 85 

84.53 

8.88 

84.50 

9.25 

84.45 

9.62 

84.41 

9.99 

85 

1 86 

85.53 

8.99 

85.49 

9.36 

85.45 

9.74 

85.40 

10.11 

86 

87 

86.52 

9.09 

86.48 

9.47 

86.44 

9.85 

86.40 

10.23 

87 

88 

87.52 

9.20 

87.48 

9.58 

87.43 

9.96 

87.39 

10.34 

88 

89 

88.51 

9.30 

88.47 

9.69 

88.43 

10.08 

88.38 

10.46 

89 

90 

89.51 

9.41 

89.47 

9.80 

89.42 

10.19 

89.38 

10.58 

90 

91 

90.50 

9.51 

90.46 

9.91 

90.42 

10.30 

90.37 

10.70 

91 

92 

91.50 

9.62 

91.45 

10.02 

91.41 

10.41 

91.36 

10.81 

92 

93 

92.49 

9.72 

92.45 

10.12 

92.40 

10.53 

92.36 

10.93 

93 

94 

93.49 

9.83 

93.44 

10.23 

93.40 

10.64 

93.35 

11.05 

94 

95 

94.48 

9.93 

94.44 

10.31 

94.39 

10.75 

94.34 

11.17 

95 

96 

95.47 

10.03 

95.43 

10.45 

95.38 

10.87 

95.33 

11.28 

96 

97 

96.47 

10.14 

96.42 

10.56 

96.38 

10.98 

96.33 

11.40 

97 

98 

97.46 

10.24 

97.42 

10.67 

97.37 

11.09 

97.32 

f 1.52 

98 

99 

98.46 

10.35 

98.41 

10.78 

98.36 

11.21 

98.31 

11.64 

99 

100 

99.45 

10.45 

99.41 

10.89 

99.36 

11.32 

99.31 

j 1.75 

100 

• 

CJ 

CJ 

R 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o ' 
c 

CD 
• •4 

Q 

84 Deg. 

83| Deg. 

83^ 

Deg. 

831 Deg. 

si 

w 

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FKAVKRSE TAULZ 



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5.95 

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7 

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6.94 

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7 


8 

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7.94 

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15.87 

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16.86 

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18 

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2.19 

17.86 

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2.35 

17.84 

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18.83 

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20.83 

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2.74 

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22 

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21.82 

2.78 

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2.87 

21.80 

2.97 

22 


23 

22 

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2.80 

22.82 

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22 

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3.00 

22.79 

3.10 

23 


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23 

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2.92 

23.81 

3.03 

23 

.79 

3.13 

23.78 

3.24 

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25 

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3.05 

24.80 

3.15 

24 

.79 

3.26 

24.77 

3.37 

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26 

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25.79 

3.28 

25 

.78 

3.39 

25.76 

3.51 

26 

7 

27 

26 

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3.29 

26.78 

3.41 

26 

.77 

3.52 

26.75 

3.64 

27 


28 

27 

.79 

3.41 

27.78 

3.53 

27 

.76 

3.65 

27.74 

3.78 

28 


29 

28 

.78 

3.53 

28.77 

3.66 

28 

.75 

3.79 

28.74 

3.91 

29 


30 

29 

.78 

3.66 

29.76 

3.79 

29 

.74 

3 92 

29.73 

4.05 

30 


31 

30 

.77 

3.78 

30.75 

3.91 

30 

.73 

4.05 

30.72 

4.18 

31 


32 

31 

.76 

3.90 

31.74 

4.04 

31 

.73 

4.IS 

31.71 

4.32 

32 

,{ 

33 

32 

.75 

4.02 

32.74 

4.16 

32 

.72 

4.31 

32.70 

4.45 

33 


34 

33 

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4.14 

33.73 

4.29 

33 

.71 

4.44 

33.69 

4.58 

34 


35 

34 

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4.27 

34 .72 

4.42 

34 

.70 

4.57 

34.68 

4.72 

35 


36 

35 

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4.39 

35.71 

4.54 

35 

.69 

4.70 

35.67 

4.85 

146 

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37 

36 

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4.51 

36.70 

4.67 

36 

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4.83 

36.66 

4.99 

37 


38 

37 

.72 

4.63 

37.70 

4.80 

37 

.67 

4.96 

37.65 

5.12 

38 


39 

38 

.71 

4.75 

38.69 

4.92 

38 

.67 

5.09 

38.64 

5.26 

39 

> 

40 

39 

.70 

4.87 

39.68 

5.05 

39 

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5.22 

39.63 

5.39 

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40.67 

5.17 

40 

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5.35 

40.63 

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41 

j 

42 

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41.66 

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5.48 

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43 

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42.66 

5.43 

42 

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5.61 

42.61 

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43 

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43.65 

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5.93 

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45 

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44.64 

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44.59 

6.07 

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46 

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45.63 

5.81 

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6.00 

45.58 

6.20 

46 


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46 

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46.62 

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6.13 

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6.34 

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5.85 

47.62 

6.06 

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6.47 

48 


49 

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48.61 

6.18 

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6.40 

48.55 

6.61 

49 


60 

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6.09 

49.60 

6.31 

49 

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6.53 

49.54 

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50 


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£3 Deg. 

82| Deg. 

82i Deg. 

82$ Deg. 



































































































TRAVERSE TARLK. 


ii 7 


o 
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7* Deg. 

7-‘ Deg. 

7£ Deg. 

a; 

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3 

O 

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Lat. 

D«p. 

Lat. 

Dep. 

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I i 

51 

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6.22 

50.59 

6.44 

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6.66 

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51.61 

6.34 

51.58 

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53 

52.60 

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56.58 

6.95 

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7.19 

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7.69 

57 

58 

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7.07 

57.54 

7.32 

57.50 

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57.47 

7.82 

53 

59 

58.56 

7.19 

58.53 

7.45 

58.50 

7.70 

58.46 

7.96 

59 

60 

59.55 

7.31 

59.52 

7.57 

59.49 

7.83 

59.45 

8.09 

60 

61 

60.55 

7.43 

00.51 

7.70 

60.48 

7.96 

60.44 

8.23 

61' 

62 

61.54 

7.56 

61.50 

7.82 

61.47 

8.09 

61.43 

8.36 

62 

63 

62.53 

7.68 

62.50 

7.95 

62.46 

8.22 

62.42 

8.50 

63 

64 

63.52 

7.80 

63.49 

8.08 

63.45 

8.35 

63.42 

8.63 

64 

65 

64.52 

7.92 

64.48 

8.20 

64.44 

8.48 

64.41 

8.77 

65 

66 

65.51 

8.04 

05.47 

8.33 

65.44 

8.Cl 

65.40 

8.90 

66 

67 

06 50 

8.17 

66.46 

8.40 

66.43 

8.75 

66.39 

9.04 

67 

68 

67.49 

8.29 

67.46 

8.58 

67.42 

8.88 

67.38 

9.17 

68 

69 

68.49 

8.41 

68.45 

8.71 

08.41 

9.01 

68.37 

9.30 

69 

70 

69.48 

8.53 

69.44 

8.83 

69.40 

9.14 

69.36 

9.44 

70 

71 

70.47 

8.65 

70.43 

8.96 

70.39 

9.27 

70.35 

9.57 

71 

72 

71.46 

8.77 

71.42 

9.09 

71.38 

9.40 

71.34 

9.71 

72 

73 

72.46 

8.90 

72.42 

9.21 

72 33 

9.53 

72.33 

9.84 

73 

74 

73.45 

9.02 

73.41 

9.34 

73.37 

9.66 

73.32 

9.98 

74 

75 

74.44 

9.14 

74.40 

9.46 

74.36 

9.79 

74.31 

10.11 

75 

76 

75.43 

9.26 

75.39 

9.59 

75.35 

9.92 

75.31 

10.25 

76 

77 

76.43 

9.38 

76.38 

9.72 

76.34 

10.05 

76.30 

10.38 

77 

78 

77.42 

9.51 

77.38 

9.84 

77.33 

10.18 

77.29 

10.52 

78 

79 

78.41 

9.63 

78.37 

9.97 

78.32 

10.31 

78.28 

10.65 

79 

80 

79.40 

9.75 

79.30 

10.10 

79.32 

10.44 

79.27 

10.79 

80 

81 

80.40 

9.87 

80.35 

10.22 

80.31 

10.57 

80.26 

10.92 

81 

82 

81.39 

9.99 

81.34 

10.35 

81.30 

10.70 

81.25 

11.06 

82 

83 

82.38 

10.12 

82.34 

10.47 

82.29 

10.83 

82.24 

11.19 

83 

84 

83.37 

10.24 

83.33 

10.60 

83.28 

10.96 

83.23 

11.33 

84 

85 

84.37 

10.36 

84.32 

10.73 

84.27 

11.09 

84.22 

11.46 

85 

86 

85.36 

10.48 

85.31 

10.85 

85.26 

11.23 

85.21 

11.60 

86 

87 

86.35 

10.60 

86.30 

10.98 

86.26 

11.36 

86.21 

11.73 

87 

88 

87.34 

10.72 

87.30 

11.11 

87.25 

11.49 

87.20 

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88 

89 

88.34 

10.85 

88.29 

11.23 

88.24 

11.62 

88.19 

12.00 

89 

90 

89.33 

10 97 

89.28 

11.36 

89.23 

11.75 

89.18 

12.14 

90 

91 

90.32 

11.09 

90.27 

11.48 

90.22 

11.88 

90.17 

12.27 

91 

92 

91.31 

11.21 

91.26 

11.61 

91.21 

12.01 

91.16 

12.41 

92 

93 

92.31 

11.33 

92.26 

11.74 

92.20 

12.14 

92.15 

12.54 

93 

94 

93.30 

11.46 

93.25 

11.86 

93.20 

12.27 

93.14 

12.68 

94 

95 

94.29 

11.58 

94.24 

11.99 

94.19 

12.40 

94.13 

12.81 

95 

96 

95.28 

11.70 

95.23 

12.12 

95.18 

12.53 

95.12 

12.95 

96 

97 

96.28 

11.82 

96.22 

12.24 

96.17 

12.66 

96.11 

13.08 

97 

98 

97.27 

11.94 

97.22 

12.37 

97.16 

12.79 

97.10 

13.22 

98 

99 

98.26 

12.07 

98.21 

12.49 

98.15 

12.92 

98.10 

13.35 

GO 

100 

99.25 

12.19 

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12.62 

99.14 

13.05 

99.09 

13.49 

100 

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82.1 Deg. 

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82$ Deg. 

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TRAVERSE TARLE. 


Distance. 

8 Deg. 

Deg. 

G-i Deg. 

8£ Deg. 

O 1 
• 

m 

r-* 

p 

3 

D 

3 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.99 

0.14 

0. 

99 

0.14 

0.99 

0.15 

0.99 

0.15 

1 

2 

1.98 

0.28 

1. 

98 

0.29 

1.98 

0.30 

1.98 

0.30 

2 

3 

2.97 

0.42 

2. 

97 

0.43 

2.97 

0.44 

2.97 

0.46 

3 

8 4 

3.90 

0.56 

3. 

96 

0.57 

3.96 

0.59 

3.95 

0.61 

4 


4.95 

0.70 

4. 

95 

0.72 

4.95 

0.74 

4.94 

0.76 

5 

6 

5.94 

0.84 

ft. 

94 

0.86 

5.93 

0.89 

5.93 

0.91 

6 

I 7 

6.93 

0.97 

6. 

93 

1.00 

6.92 

1.03 

6.92 

1.06 

7 

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7.92 

1.11 

7. 

92 

1.15 

7.91 

1.18 

7.91 

1 22 

9 

1 9 

8.91 

1.25 

8. 

91 

1.29 

8.90 

1.33 

8.90 

1.37 

9 

10 

9.90 

1.39 

9. 

90 

1.43 

9.89 

1.48 

9.88 

1.52 i 

10 

11 

10.89 

1.53 

10. 

89 

1.58 

10.88 

1.63 

10.87 

1.67 

11 

12 

11.88 

1.67 

11. 

88 

1.72 

11.87 

1.77 

11.86 

1.83 

12 

13 

12.87 

1.81 

12. 

87 

1.87 

12.86 

1.92 

12.85 

1.98 

13 

14 

13.86 

1.95 

13. 

86 

2.01 

13.85 

2.07 

13.84 

2.13 

14 : 

15 

14.85 

2.09 

14. 

85 

2.15 

14.84 

9 oo 

14.83 

2.28 

15 

16 

15.84 

2.23 

15. 

84 

2.30 

15.82 

2.36 

15.81 

2.43 

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17 

16.83 

2.37 

16. 

83 

2.44 

16.81 

2.51 

16.80 

2.59 

17 ! 

IS 

17.82 

2.51 

17. 

81 

2.53 

17.80 

2.66 

17.79 

2.74 

18 

19 

18.82 

2.64 

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80 

2.73 

18.79 

2.81 

18.78 

2.89 

19 

20 

19.81 

2.78 

19. 

79 

2.87 | 

19.78 

2.96 

19.77 

3.04 

20 

21 

20.80 

2.92 

20. 

78 

3.01 1 

20.77 

3.10 1 

20.76 

3.19 

21 

22 

21.79 

3.06 

21. 

77 

3.16 

21.76 

3.25 

21.74 

3.35 

22 i 

23 

22.78 

3.20 

22. 

76 

3.30 

22.75 

3.40 

22.73 

3.50 

23 i 

24 

23.77 

3.34 

23. 

75 

3.44 

23.74 

3.55 

23.72 

3.65 

24 | 

25 

24.76 

3.48 

24. 

74 

3.59 

24.73 

3.70 

24.71 

3.80 

25 ; 

20 

25.75 

3.62 

25. 

73 

3.73 

25.71 

3.84 

25.70 

3.96 

26 1 

27 

26.74 

3.76 

26. 

72 

3.87 

26.70 

3.99 

26.69 

4.11 

27 | 

28 

27.73 

3.90 

27. 

71 

4.02 

27.69 

4.14 

27.67 

4.26 

28 i 

29 

28.72 

4.04 

28. 

70 

4.16 

28.68 

4.29 

28.66 

4.41 

29 [ 

30 

29.71 

4.18 

29. 

69 

4.30 

29.67 

4.43 

29.65 

4.56 

30 ; 

31 

30.70 

4.31 

30. 

68 

4.45 

30.66 

4.58 

30.64 

4.72 

31 ! 

32 

31.69 

4.45 

31. 

67 

4.59 

31.65 

4.73 

31.63 

4.87 

32 

33 

32.68 

4.59 

32. 

66 

4.74 

32.6; 

4.S8 

32.62 

5.02 

33 

34 

33.67 

4.73 

33. 

65 

4.88 

33.63 

5.03 

33.60 

5.17 

34 

35 

34.66 

4.87 

34. 

64 

5.02 

34.62 

5.17 

34.59 

5.32 

35 

36 

35.65 

5.01 

35 

63 

5.17 

35.60 

5.32 

35.58 

5.48 

36 

37 

36.64 

5.15 

36 

62 

5.31 

36.59 

5.47 

36.57 

5.63 

37 

38 

37.63 

5.29 

37. 

.61 

5.45 

37.58 

5.62 

37.56 

5.78 

38 

39 

38.62 

5.43 

38 

.60 

5.60 

38.57 

5.76 

38.55 

5.93 

39 

40 

39.61 

5.57 

39- 

59 

5.74 

39.56 

5.91 

39.53 

6.08 

40 

41 

40.60 

5.71 

40 

,58 

5.88 

40.55 

6.06 

40.52 

6.24 

41 

42 

41.59 

5.85 

41 

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6.03 

41.54 

6.21 

41.51 

6.39 

42 

43 

42.58 

5.98 

42 

.56 

6.17 

42.53 

6.36 

42.50 

6.54 

43 

44 

43.57 

6.12 

43 

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6.31 

43.52 

6.50 

43.49 

6.69 

44 

45 

44.56 

6.26 

44 

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6.46 

44.51 

6.65 

44.48 

6.85 

45 

46 

45.55 

6.40 

45 

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G.60 

45.49 

6.80 

45.46 

7.00 

46 

47 

46.54 

6.54 

46 

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6.74 

46.48 

6.95 

146.45 

7.15 

47 

48 

47.53 

6.68 

47 

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6.89 

47.47 

7.09 

47.44 

7.30 

48 

49 

48.52 

6.82 

48 

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7.03 

48.46 

7.24 

48.43 

7.45 

49 

50 

49.51 

6.96 

49 

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7.17 

49.45 

7.39 

49.42 

7.61 

50 

Distance.| 

Dep. 

Liit* 

Dep. 

Lat. 

Dep. 

L^ti 

Dep. 

Lat. 

Distance. 

82 Deg. 

011 Deg. 

84 

Deg. 

814 Deg. 

1 














































































































TRAVERSE TABLE 


19 


c l 

*— 

cc 

f* 

P 

D 

O 

C3 

8 Deg. 

3} Deg. 

8£ Deg. 

8f Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.50 

7.10 

50.47 

7.32 

60.44 

7.54 

50.41 

7.76 

51 

52 

51.49 

7.24 

51.46 

7.46 

51.43 

7.69 

51.39 

7.91 

52 

53 

52.48 

7.38 

52.45 

7.61 

52.42 

7.83 

52.38 

8.06 

53 

54 

53.47 

7.52 

53.44 

7.75 

53.41 

7.98 

53.37 

8.21 

54 

55 

54.46 

7.65 

54.43 

7.89 

54.40 

8.13 

54.36 

8.37 

55 

56 

55.48 

7.79 

55.42 

8.04 

55.38 

8.28 

55.35 

8.52 

56 

57 

56.45 

7.93 

56.41 

8.18 

56.37 

8.43 

56.34 

8.67 

57 

58 

57.44 

8.07 

57.40 

8.32 

57.36 

8.57 

57.32 

8.82 

58 

59 

58.43 

8.21 

58.39 

8.47 

58.35 

8.72 

58.31 

8.98 

59 

60 

59.42 

8.35 

59 .38 

8.61 

59.34 

8.87 

59.30 

9.13 

60 

61 

60.41 

8.49 

60.37 

8.75 

60.33 

9.02 

60.29 

9.28 

61 

62 

61.40 

8.63 

61.36 

8.90 

61.32 

9.16 

61.28 

9.43 

62 

63 

62.39 

8.77 

62.35 

9.04 

62.31 

9.31 

62.27 

9.58 

G3 

64 

63.38 

8.91 

63.34 

9.18 

63.30 

9.46 

63.26 

9.74 

64 

65 

64.37 

9.05 

64.33 

9.33 

64.29 

9.61 

64.24 

9.89 

65 

66 

65.36 

9.19 

65.32 

9.47 

65.28 

9.76 

65.23 

10.04 

66 

67 

66.35 

9.32 

66.31 

9.61 

66.26 

S.90 

66.22 

10.19 

67 

68 

67.34 

9.46 

67.30 

9.76 

67.25 

10.05 

67.21 

10.34 

68 

69 

68.33 

9.60 

68.29 

9.90 

68.24 

10.20 

68.20 

10.50 

69 

70 

69.32 

8.74 

69.28 

10.04 

69.23 

10.35 

69.19 

10.65 

70 

71 

70.31 

9.88 

70.27 

10.19 

70.22 

10.49 

70.17 

10.80 

71 

72 

71.30 

10.02 

71.25 

10.33 

71.21 

10.64 

71.16 

10.95 

72 

73 

72.29 

10.16 

72.24 

10.47 

72.20 

10.79 

72.15 

11.10 

73 

74 

73.28 

10.30 

73.23 

10.62 

73.19 

10.94 

73.14 

11.26 

74 

75 

74.27 

10.44 

74.22 

10.76 

74.18 

11.09 

74.13 

11.41 

75 

76 

75.26 

10.58 

75.21 

10.91 

75.17 

11.23 

75.12 

11.56 

76 

77 

76.25 

10.72 

76.20 

11.05 

76.15 

11.38 

76.10 

11.71 

77 

78 

77.24 

10.86 

77.19 

11.19 

77.14 

11.53 

77.09 

11.87 

78 

79 

78.23 

10.99 

78.18 

11.34 

78.13 

11.68 

78.08 

12.02 

79 

80 

79.22 

11.13 

79.17 

11.48 

79.12 

11.82 

79.07 

12.17 

80 

81 

80.21 

11.27 

80.16 

11.62 

80.11 

11.97 

80.06 

12.32 

81 

82 

81.20 

11.41 

81.15 

11.77 

81.10 

12.12 

81.05 

12.47j 

82 

83 

82.19 

11.55 

82.14 

11.91 

82.09 

12.27 

82.03 

12.63 

83 

84 

83.18 

11.69 

83.13 

12.05 

83.08 

12.42 

83.02 

12.78 

84 

85 

84.17 

11.83 

84.12 

12.20 

84. O' 7 

12.56 

84.01 

12.93 

85 

86 

85.16 

11.97 

85.11 

12.34 

85.06 

12.71 

85.00 

13.08 

86 

87 

86.15 

12.11 

86.10 

12.48 

86.04 

12.86 

85.99 

13.23 

87 

88 

87.14 

12.25 

87.09 

12.63 

87.03 

13.01 

86.98 

13.39 

88 

89 

88.13 

12.39 

88.08 

12.77 

88.02 

13.16 

87.96 

13.54 

89 

90 

69.12 

12.53 

89.07 

12.91 

89.01 

13.30 

88.95 

13.69 

90 

31 

90.11 

12.66 

90.06 

13.06 

90.00 

13.45 

89.94 

13.84 

91 

92 

91.10 

12.80 

91.05 

13.20 

90.99 

13.60 

90.93 

14.00 

92 

93 

92.09 

12.94 

92.04 

13.34 

91.98 

13.75 

91.92 

14.15 

93 

94 

93.09 

13.08 

93.03 

.13.49 

92.97 

13.89 

92.91 

14.30 

94 

95 

94.08 

13.22 

94.02 

13.63 

93.96 

14.04 

93.89 

14.45 

95 

96 

95.07 

13.36 

95.Oi 

13.78 

94.95 

14.19 

94.88 

14.00 

96 

97 

96.06 

13.50 

96.00 

13.92 

95.93 

14.34 

95.87 

14.76 

97 

98 

97.05 

13.64 

96.99 

14.06 

96.92 

14.49 

96.86 

14.91 

98 

99 

98.04 

13.78 

97.98 

14.21 

97.91 

14.63 

97.85 

15.06 

99 

100 

99.03 

13.92 

98.97 

14.35 

98.90 

14.78 

98.84 

15.21 

100 

05 

/■' 

s 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

V 

9 

S 

ri 

91 

a 

82 Deg. 

fill Deg. 

t 

81f Deg. 

81| Deg. 

| 

W 

C/1 

• 

Q 






































































































20 


TRAVERSE TABLE 


Distance. 

' 

9 Deg. 

9$ Deg. 

n 

Deg. 

9.f Deg 

C 

tn 

r. 

P 

2 

o 

a 

• 

Lat. 

Dep. 

Lftt • 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.99 

0. 

16 

0.99 

0. 

16 

0.99 

0.17 

0.99 

0 

.17 

1 

2 

1.98 

0 

31 

1.97 

0. 

32 

1.97 

0.33 

1.97 

0 

.34 

2 

3 

2.96 

0. 

47 

2.96 

0. 

49 

2.96 

0.50 

2.96 

0 

.51 

3 

4 

3.95 

0. 

63 

3.95 

0. 

04 

3.95 

0.66 

3.94 

0 

.68 

4 

6 

4.94 

0. 

78 

4.93 

0. 

80 

4.93 

0.S3 

4.93 

0 

.85 

5 

C 

5.93 

0. 

94 

5.92 

0. 

96 

5.92 

0.99 

5.91 

1 

.02 

n 

7 

6.91 

1. 

10 

G.91 

1. 

13 

6.90 

1.16 

6.90 

1 

.19 

7 

8 

7.90 

1. 

25 

7.90 

1. 

29 

7.89 

1.32 

7.88 

1 

.35 

8 

9 

8.89 

1. 

41 

8.88 

1. 

45 

8.88 

’..49 

8.87 

* 

.52 

0 

10 

9.83 

1. 

56 

9.87 

1. 

61 

9.86 

1 • \J*J 

S. oG 

i 

.69 

10 

11 

10.86 

1. 

72 

10.86 

1. 

77 

10.85 

1.82 

10.84 

1 

.86 

11 

12 

11.85 

1. 

88 

11.84 

1. 

93 

11.84 

1.98 

11.83 

2 

.03 

12 

13 

12.84 

2. 

03 

12.83 

2. 

09 

12.82 

2.15 

12.81 

2 

.20 

13 

14 

13.83 

2. 

19 

13.82 

2. 

25 

13.81 

2.31 

13.80 

2 

.37 

14 

15 

14.82 

2. 

35 

14.80 

O 

• 

41 

14.79 

2.48 

14.78 

2 

.54 

15 

16 

15.80 

O 

/V 

50 

15.79 

2. 

57 

15.78 

2.64 

15.77 

2 

.71 

16 

17 

16.79 

O 
/w • 

66 i 

16.78 

2. 

73 

16.77 

2.81 

16.75 

2 

.88 

17 

18 

17.78 

2. 

82 1 

17.77 

2. 

89 

17.75 

2.97 

17.74 

3 

.05 

18 

19 

18.77 

2. 

97 

18.75 

3. 

05 

18.74 

3.14 

18.73 

3 


19 

20 

19.75 

3. 

13 

! 

19.74 

3. 

21 

19.73 

3.30 

19.71 

3 

.39 

20 

21 

20.74 

3. 

29 | 

20.73 

3. 

38 

20.71 

3.47 

20.70 

3 

.56 

21 

22 

21.73 

3. 

44 

21.71 

3. 

54 

21.70 

3.63 

21.68 

3 

.73 

22 

23 

22.72 

3. 

60 

22.70 

3. 

70 

22.68 

3.80 

22.67 

3 

.90 

23 

24 

23.70 

3. 

75 

23.69 

3. 

86 

23.67 

3.96 

23.65 

4 

.06 

24 

25 

24.69 

3. 

91 

24.67 

4. 

02 

24.66 

4.13 

24.64 

4 

.23 

25 

26 

25.68 

4. 

07 

25.66 

4. 

18 

25.64 

4.29 

25.62 

4 

.40 

26 

27 

26.67 

4. 

22 

26.65 

4. 

34 

26.63 

4.46 

26.61 

4 

.57 

27 

28 

27.66 

4. 

38 

27.64 

4. 

50 

27.62 

4.62 

27.60 

4 

.74 

28 

29 

28.64 

4. 

54 

28.62 

4. 

66 

28.60 

4.79 

28.58 

4 

.91 

29 

30 

29.63 

4. 

69 

29.61 

4. 

82 

29.59 

4.95 

29.57 

5 

.03 

30 

31 

30.62 

4. 

85 

30.80 

4. 

98 

30.57 

5.12 

30.55 

5 

.25 

31 

32 

31.61 

5. 

01 

31.58 

5. 

14 

31.56 

5.28 

31.54 

5 

.42 

32 

33 

32.59 

5. 

16 

32.57 

5. 

30 

32.55 

5.45 

32.52 

5 

.59 

33 

34 

33.58 

5. 

32 

33.56 

5. 

47 

33.53 

5.61 

33.51 

5 

.76 

34 

35 

34.57 

5. 

48 

34.54 

5. 

63 

34.52 

5.78 

34.49 

5 

.93 

35 

36 

35.56 

5. 

63 

35.53 

5. 

79 

35.51 

5.94 

35.48 

6 

.10 

36 

37 

36.54 

5. 

79 

36.62 

5. 

95 

36.49 

6.11 

36.47 

6 

.27 

37 

38 

37.53 

5. 

94 

37.51 

6. 

11 

37.48 

6.27 

37.45 

6 

.44 

38 

39 

38.52 

6. 

10 

38.49 

6. 

27 

38.47 

6.44 

38.44 

6 

.60 

39 

40 

39.51 

6. 

26 

39.48 

6 . 

43 

39.45 

6.60 

39.42 

6 

.77 

40 

41 

40.50 

6 . 

41 

40.47 

6. 

59 

40.44 

6.77 

40.41 

6 

.94 

41 

42 

41.48 

6. 

57 

41.45 

6. 

75 

41.42 

6.92 

41.39 

7 

.11 

42 

43 

42.47 

6. 

73 

42.44 

6. 

91 

42.41 

7.10 

42.38 

7 

.28 

43 

44 

43.46 

6. 

88 

43.43 

7. 

07 

43.40 

7.26 

43.36 

7 

.45 

44 

45 

44.45 

7. 

04 

44.41 

7. 

23 

44.38 

7.43 

44.35 

7 

.62 

45 

46 

45.43 

7. 

20 

45.40 

7. 

39 

45.37 

7.59 

45.341 

7 

.79 

16 

47 

46.42 

7. 

35 

46.39 

7. 

55 

46.36 

7.76 

46.32 

7 

.96 

17 

48 

47.41 

7. 

51 

47.38 

7. 

72 

47.34 

7.92 

47.31 

8 

.13 

48 

49 

48.40 

7. 

67 

48.36 

7. 

88 

48.33 

8.09 

48.29 

8 

.30 

49 

50 ' 

49.38 

7. 

82 

49.35 

8. 

04 

49.32 

8.25 

49.28 

8 

.47 

50 

© 

© 

a 

o3 

CO 

Q 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i c; 

Q 

a 

« 

.a 

ft 

81 Deg. 

80f Deg. 


Deg. 

80$ Deg. 






























































































TllAVEKSE TABLE 


21 


o 

!-► 

P3 

9 Deg. 

94 Deg. 

j Deg. 

9.f Deg. 

o 

H • 

oc 

r* 

p 

P 

o 

® 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

p 

a 

a 

51 

50.37 

7.98 

50.34 

8.20 

50.30 

8.42 

50.26 

8.64 

‘51 

52 

51.36 

8.13 

51.32 

8.36 

51.29 

8.58 

j 51.25 

8.81 

52 

53 

52.35 

8.29 

52.31 

8.52 

52.27 

8.75 

52.23 

8.98 

53 

54 

53.34 

8.45 

53.30 

8.68 

53.26 

8.91 

53.22 

9.14 

54 

65 

54.32 

8.60 

54.28 

8.84 

54.25 

9.08 

54.21 

9.31 

55 

66 

55.31 

8.76 

55.27 

9.00 

55.23 

9.24 

55.19 

9.48 

56 

67 

50 . 30 

8.92 

56.26 

9.16 

56.22 

9.41 

56.18 

9.65 

57 

58 

57.29 

9.07 

57.25 

9.32 

57.20 

9.57 

57.16 

9.82 

58 

59 

58.27 

9.23 

58.23 

9 48 

58.19 

9.74 

58.15 

9.99 

59 

60 

59.26 

9.39 

59.22 

9 64 

59.18 

9.90 

59.13 

10.16 

60 

61 

60.25 

9.54 

60.21 

9.81 

60.16 

10.07 

60.12 

10.33 

61 

62 

61.24 

9.70 

61.19 

9.97 

61.15 

10.23 

61 .10 

10.50 

62 

63 

62.22 

9.86 

62.18 

10.13 

62.14 

10.40 

62.09 

10.67 

63 

64 

63.21 

10.01 

63.17 

10.29 

63.12 

10.56 

63.08 

10.84 

64 

65 

64.20 

10.17 

64.15 

10.45 

64.11 

10.73 

64.06 

11.01 

65 

66 

65.19 

10.32 

65.14 

10.61 

65.09 

10.89 

65.05 

11.18 

G6 

67 

66.18 

10.48 

66.13 

10.77 

66.08 

11.06 

66.03 

11.35 

67 

68 

67.16 

10.64 

67.12 

10.93 

67.07 

11.22 

67.02 

11.52 

68 

69 

68.15 

10.79 

68.10 

11.09 

68.05 

11.39 

68.00 

11.69 

69 

70 

69.14 

10.95 

69.09 

11.25 

69.04 

11.55 

68.99 

11.85 

70 

71 

70.13 

11.li 

70.08 

11.41 

70.03 

11.72 

69.97 

12.02 

71 

72 

71.11 

11.26 

71.06 

11.57 

71.01 

11.88 

70.96 

12.19 

72 

73 

72.10 

11.42 

72.05 

11.73 

72.00 

12.05 

71.95 

12.36 

73 

74 

73.09 

11.58 

73.04 

11.89 

72.99 

12.21 

72.93 

12.53 

74 

75 

74.08 

11.73 

74.02 

12.06 

73.97 

12.38 

73.92 

12.70 

75 

76 

75.06 

11.89 

75.01 

12.22 

74.96 

12.54 

74.90 

12.87 

76 

77 

76.05 

12.05 

76.00 

12.38 

75.94 

12.71 

75.89 

13.04 

77 

78 

77.04 

12.20 

76.99 

12.54 

76.93 

12.87 

76.87 

13.21 

78 

79 

78.03 

12.36 

77.97 

12.70 

77.92 

13.04 

177.86 

13.38 

79 

80 

79.02 

12.51 

78.96 

12.86 

78.90 

13.20 

|78.84 

13.55 

80 

81 

80.00 

12.67 

79.95 

13.02 

79.89 

13.37 

j 79.83 

13.72 

81 

82 

80.99 

12.83 

80.93 

13.18 

80.88 

13.53 

80.82 

13.89 

82 

63 

81.98 

12.98 

81.92 

13.34 

81.86 

13.70 

181.80 

14.06 

83 

84 

82.97 

13.14 

82.91 

13.50 

82.85 

13.86 

82.79 

14.23 

84 

85 

83.95 

13.30 

83.89 

13.66 

83.83 

14.03 

83.77 

14.39 

85 

86 

84.94 

13.45 

84.88 

13.82 

84.82 

14.19 

84.76 

14.56 

86 

87 

85.93 

13.61 

85.87 

13.98 

85.81 

14.36 

!85.74 

14.73 

87 

88 

86.92 

13.77 

86.86 

14.15 

86.79 

14.52 

|86.73 

14.90 

88 

89 

87.90 

13.92 

87.84 

14.31 

87.78 

14.69 

!87.71 

15.07 

89 

90 

88.89 

14.08 

88.83 

14.47 

88.77 

14.85 

!88.70 

15.24 

90 

91 

89.88 

14.24 

89.82 

14.63 

89.75 

15.02 

89.69 

15.41 

91 

92 

90.87 

14.39 

90.80 

14.79 

90.74 

15.18 

90 67 

15.58 

92 

93 

91.86 

14.55 

91.79 

14.95 

91.72 

15.35 

91.66 

15.75 

93 

94 

92.84 

14.70 

92.78 

15.11 

92.71 

15.51 

92.64 

15.92 

91 

95 

93.83 

14.86 

93.76 

15.27 

93.70 

15.68 

93.63 

16.09 

95 

96 

94.82 

15.02 

94.75 

15.43 

94.68 

15.84 

94.61 

16.26 

96 

97 

95.81 

15.17 

95.74 

15.59 

95.67 

16.01 

95.60 

16 43 

97 

98 

96.79 

15.33 

96.73 

15.75 

96.66 

16.17 

96.58 

16.60 

98 

99 

97.78 

15.49 

97.71 

15.91 

97.64 

1 ft O A 

1 V/ • I/'t 

97.57 

16.77 

99 

100 

98.77 

15.64 

98.70 

16.07 

98.63 

16.50 

98.56 

16.93 

100 

• 

O 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

cd 

•-» 

00 

o 

81 Deg. 

80f Deg. 

80£ Deg. 

80.} Deg. 





















































































22 


TRAVERSE TABLE 


Distance. 

10 Deg. 

10} Deg. 

10} 

1 

Deg. 

10} Deg. 

Distance.i 

i 

I Jilt. 

Dep. 

Liit. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0*98 

0.17 

0.98 

0.18 

0.98 

0.18 

0.98 

0.19 

1 

2 

1.97 

0.35 

1.97 

0.36 

1.97 

0.36 

1.96 

0.37 

2 

3 

2.95 

0.52 

2.95 

0.53 

2.95 

0.55 

2.95 

0 56 

3/ 

4 

3.94 

0.69 

3.94 

0.71 

3.93 

0.73 

3.93 

0.75 

41 

5 

4.92 

0.87 

4.92 

0.89 

4.92 

0.91 

4.91 

0. 93 


6 

5.91 

1.04 

5.90 

1.07 

5.90 

1.09 

5.89 

]\ 12 

61 

7 

6.89 

1.22 

6.89 

1.25 

6.88 

1.28 

5.88 

1.31 

7 

8 

7.88 

1.39 

7.87 

1.42 

7.87 

1.46 

7,86 

1.49 

6 

9 

8.86 

1.56 

8.86 

1.60 

8.85 

1.64 

8.84 

1.68 

9 

10 

9.85 

1.74 

9.84 

1.78 

9.83 

1.82 

9.82] 

1.87 

10 

11 

10.83 

1 .91 

10.82 

1.96 

10.82 

2.00 

10.81 

2.05 

11 

12 

11.82 

2.08 

11.81 

2.14 

11.80 

2.19 

11.79 

2.24 

12 

13 

12.80 

2.26 

12.79 

2.31 

12.78 

2.37 

12.77 

2.42 

13 

14 

13.79 

2.43 

13.78 

2.49 

13.77 

2.55 

13.75 

2.61 

14 

15 

14.77 

2.60 

14.76 

2.67 

14.75 

2.73 

14.74 

2.80 

15 

16 

15.76 

2.78 

15.74 

2.85 

15.73 

2.92 

15.72 

2.98 

16 

17 

16.74 

2.95 

16.73 

3.03 

16.72 

3.10 

16.70 

3.17 

17 

18 

17.73 

3.13 

17.71 

3.20 

17.70 

3.28 

17.68 

3.36 

18 

19 

18.71 

3.30 

18.70 

3.38 

18.68 

3.46 

18.67 

3.54 

19 

20 

19.70 

3.47 

19.68 

3.56 

19.67 

3.64 

19.65 

3.73 

20 

21 

20.68 

3.65 

20.66 

3.74 

20.65 

3.83 

20.63 

3.92 

21 

22 

21.67 

3.82 

21.65 

3.91 

21.63 

4.01 

21.61 

4.10 

. 22 

23 

22.65 

3.99 

22.63 

4.09 

22.61 

4.19 

22.60 

4 .29 

23 

24 

23.64 

4.17 

23.62 

4.27 

23.60 

4.37 

23.58 

4.48 

24 

25 

24.62 

4-34 

24.60 

4.45 

24.58 

4.56 

24.56 

4.66 

25 

26 

25.61 

4.51 

25.59 

4.63 

25.56 

4.74 

25.54 

4.85 

26 

27 

26.59 

4.69 

26.57 

4.80 

26.55 

4.92 

26.53 

5.04 

27 

28 

27.57 

4.86 

27.55 

4.98 

27.53 

5.10 

27.51 

5.22 

28 

29 

28.56 

5.04 

28.54 

5.16 

28.51 

5.28 

28.49 

5.41 

29 

30 

29.54 

5.21 

29.52 

5.34 

29.50 

5.47 

29.47 

5.60 

30 

31 

30.53 

5.38 

30.51 

5.52 1 

30.48 

5.65 

30.46 

5.78 

31 

32 

31.51 

5.56 

31.49 

5.69 

31.46 

5.83 

31.44 

5.97 

32 

33 

32.50 

5.73 

32.47 

5.87 

32.45 

6.01 

32.42 

6.16 

33 

34 

33.48 

5.90 

33.46 

6.05 

33.43 

6.20 

33.40 

6.34 

34 

35 

34.47 

6.08 

34.44 

6.23 

34.41 

6.38 

34.39 

6.53 

35 

36 

35.45 

6.25 

35.43 

6.41 

35.40 

6.56 

35.37 

6.71 

36 

37 

36.44 

6.42 

36.41 

6.58 

36.38 

6.74 

36.35 

6.90 

37 

38 

37.42 

6.60 

37.39 

6.76 

37.36 

6.92 

37.33 

7.09 

38 

39 

38.41 

6.77 

38.38 

6.94 

38.35 

7.11 

38.32 

7.27 

39 

40 

39.39 

6.95 

39.36 

7.12 

39.33 

7.29 

39.30 

7.46 

40 

41 

40.38 

7.12 

40.35 

7.30 

40.31 

7.47 

40.28 

7.65 

4 1 

42 

41.36 

7.29 

41.33 

7.47 

41.30 

7.65 

41.26 

7.83 

42 

43 

42.35 

7.47 

42.31 

7.65 

42.28 

7.84 

42.25 

8.02 

43 

44 

43.33 

7.64 

43.30 

7.83 

43.26 

8.02 

43.23 

8.21 

44 

45 

44.32 

7.81 

44.28 

8.01 

44.25 

8.20 

44.21 

8.39 

45 

46 

45.30 

7.99 

45.27 

8.19 

45.23 

8.38 

45.19 

8.58 

46 

47 

46.29 

8.16 

46.25 

8.36 

46.21 

8.57 

46.18 

8.77 

47 

48 

j 47.27 

8.34 

47.23 

8.54 

47.20 

8.75 

47.16 

8.95 

4S 

49 

148.26 

8.51 

48.22 

8.72 

48.18 

8.93 

48.14 

9.14 

49 

60 

149.24 

8.68 

49.20 

8.90 

49.16 

9.11 

49.12 

9.33 

50 

P Distance.' 

Dep. 

Lat. 

Dep. 

Lj;. 

Dep. 

Lat. 

Dep. 

Lat. 

V 

V 

c 

$ 

M 

5 

| 80 Deg. 

79} Deg. 

791 Deg. 

79} Deg. 











































































































TRAVERSE 1AI5LE. 


23 


Dista 

10 Deg. 

10i Deg. 

101 

Deg. 

101 Deg. 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep, 

61 

50.23 

8.86 

50.19 

9.08 

50.15 

9.29 

50.10 

9.51 

52 

51.21 

9.03 

51.17 

9.25 

51.13 

9.48 

51.09 

9 70 

53 

52.19 

9.20 

52.15 

9.43 

52.11 

9.66 

52.07 

9.89 

54 

53.18 

9.38 

53.14 

9.61 

53.10 

9.84 

53.05 

10.07 

55 

54.16 

9.55 

54.12 

9.79 

54.08 

10.02 

54.03 

10.26 

56 

55.15 

9.72 

55.11 

9.96 

55.06 

10.21 

55.02 

10.45 

57 

56.13 

9.90 

56.09 

10.14 

56.05 

10.39 

56.00 

10.63 

58 

57.12 

10.07 

57.07 

10.32 

57.03 

10.57 

56.98 

10.82 

59 

58.10 

10.25 

58.06 

10.50 

58.01 

10.75 

57.96 

11.00 

69 

59.09 

10.42 

59.04 

10.68 

59.00 

10.93 

58.95 

11.19 

61 

60.07 

10.59 

60.03 

10.85 

59.98 

11.12 

59.93 

11.38 

62 

61.06 

10.77 

61.01 

11.03 

60.96 

11.30 

60.91 

11.56 

63 

62.04 

10.94 

61.99 

11.21 

61.95 

11.48 

61.89 

11.75 

64 

63.03 

11.11 

62.98 

11.39 

62.93 

11.66 

62.88 

11.94 

65 

64.01 

11.29 

63.96 

11.57 

63.91 

11.85 

63.86 

12.12 

66 

65.00 

11.46 

64.95 

11.74 

64.89 

12.03 

64.84 

12.31 

67 

65.98 

11.63 

65.93 

11.92 

65.88 

12.21 

65.82 

12.50 

68 

66.97 

11.81 

66.91 

12.10 

66.86 

12.39 

66.81 

12.68 

69 

67.95 

11.98 

67.90 

12.28 

67.84 

12.57 

67.79 

12.87 

70 

68.94 

12.16 

68.88 

12.46 

68.83 

12.76 

68.77 

13.06 

71 

69.92 

12.33 

69.87 

12.63 

69.81 

12.94 

69.75 

13.24 

72 

70.91 

12.50 

70.85 

12.81 

70.79 

13.12 

70.74 

13.43 

73 

71.89 

12.68 

71.83 

12.99 

71.78 

13.30 

71.72 

13.62 

74 

72.88 

12.85 

72.82 

13.17 

72.76 

13.49 

72.70 

13.80 

75 

73.86 

13.02 

73.80 

13.35 

73.74 

13.67 

73.68 

13.99 

76 

74.85 

13.20 

74.79 

13.52 

74.73 

13.S5 

74.67 

14.18 

77 

75.83 

13.37 

75.77 

13.70 

75.71 

14.03 

75.65 

14.36 

78 

76.82 

13.54 

76.76 

13.88 

76.69 

14.21 

76.63 

14.55 

79 

77.80 

13.72 

77.74 

14.06 

77.68 

14.40 

77.61 

14.74 

80 

78.78 

13.89 

78.72 

14.24 

78.66 

14.58 

78.60 

14.92 

81 

79.77 

14.07 

79.71 

14.41 

79.64 

14.76 

79.58 

15.11 

82 

80.75 

14.24 

80.69 

14.59 

80.63 

14.94 

80.56 

15.29 

83 

81.74 

14.41 

81.68 

14.77 

81.61 

15.13 

81.54 

15.48 

84 

82.72 

14.59 

82.66 

14.95 

82.59 

15.31 

82.53 

15.67 

85 

83.71 

14.76 

83.64 

15.13 

83.58 

15.49 

83.51 

15.85 

86 

84.69 

14.93 

84.63 

15.30 

84.56 

15.67 

84.49 

16.04 

87 

85.68 

15.11 

85.61 

15.48 

85.54 

15.85 

85.47 

16.23 

88 

86.66 

15.28 

86.60 

15.66 

86.53 

16.04 

86.46 

16.41 

89 

87.65 

15.45 

87.58 

15.84 

87.51 

16.22 

87.44 

16.60 

90 

88.63 

15.63 

88.56 

16.01 

88.49 

16.40 

83.42 

16.79 

91 

89.62 

15.80 

89.55 

16.19 

89.48 

16.53 

89.40 

16.97 

92 

90.60 

15.98 

90.53 

16.37 

90.46 

16.77 

90.39 

17.16 

93 

91.59 

16.15 

91.52 

16.55 

91.44 

16.95 

91.37 

17.35 

94 

92.57 

16.32 

92.50 

16.73 

92.43 

17.13 

92.35 

17.53 

95 

93.56 

16.50 

93.48 

16.90 

93.41 

17.31 

93.33 

17.72 

96 

94.54 

16.67 

94.47 

17.08 

94.39 

17.49 

94.32 

17.91 

97 

95.53 

16.84 

95.45 

17.26 

95.38 

17.68 

95.30 

18.09 

98 

96.51 

17.02 

96.44 

17.44 

96.36 

17.86 

96.28 

18.28 

99 

97.50 

17.19 

97.42 

17.62 

97.34 

18.04 

97.26 

18.47 

100 

98.48 

17.36 

98.40 

17.79 

98.33 

18.22 

98.25 

18.65 

Q) 

O 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. j 

ei 
■*-> 

QO 

80 Deg. 

791 Deg. 

791 

Deg. 

i 

79) Deg. 

i ! 


Distance. ©<oc£>o<r>o«js£>«cno[<oaoaoaoaoaoacaoaoao o m cn cn o» a» zp cw w» aii'aou'BisifT 

O CO 00 -si Cl CJl tU C*D *3 '11 O CO 00 <1 05 m 4*. £0 *0 ►— O CO 00 <? 05 Oi >£>• CO tS OOOOviOJO'i^MMi- O CO 00 -s} © Zfl CO *0 ■— < • 























































































24 


TRAVERSE TABLE 


o 

Z 

r*- 

11 Deg. 

lli Deg. 

1 

lli 

Deg. 

Ilf Deg. 

a 

z* 

r* 

P? 

3 

a 

o 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

» 

• 

1 

0.93 

0.19 

0.98 

0.20 

0.98 

0.20 

0.98 

0.20 

1 

2 

1.9G 

0.38 

1.96 

0.39 

1.90 

0.40 

1.96 

0.41 

2 

3 

2.94 

0.57 

2.94 

0.59 

2.94 

0.60 

2.94 

0.61 

3 

4 

3.93 

0.76 

3.92 

0.78 

3.92 

0.80 

3.92 

0.82 

4 

5 

4.91 

0.95 

4.90 

0.98 

4.90 

1.00 

4.90 

1.02 

5 

G 

5.89 

1.14 

5.88 

1.17 

5.88 

1.20 

5.87 

1.22 

6 

7 

0.87 

1.34 

0.87 

1.37 

6.86 

1.40 

6.85 

1.43 

7 

8 

7.85 

1.53 

7.85 

1.56 

7.84 

1.59 

7.83 

1.63 

8 

9 

8.83 

1.72 

8.83 

1.70 

8.82 

1.79 

8.81 

1.83 

9 

10 

9.82 

1.91 

9.81 

1.95 

9.80 

1.99 

9.79 

2.04 

10 

11 

10.80 

2.10 

10.79 

2.15 

10.78 

2. 19 

10.77 

2.24 

11 

12 

11.78 

2.29 

11.77 

2.34 

11.76 

2.39 

11.75 

2.44 

12 

13 

12.76 

2.48 

12.75 

2.54 

12.74 

2.59 

12.73 

2.65 

13 

14 

13.74 

2 07, 

13.73 

2.73 

13.72 

2.79 

13.71 

2.85 

14 

15 

14.72 

2.80 

14.71 

2.93 

14.70 

2.99 

14.69 

3.06 

15 

10 

15.71 

3.95 

15.09 

3.12 

15.08 

3.19 

15.66 

3.26 

16 

17 

10.69 

3.24 

16.67 

3.32 

10.66 

3.39 

16.64 

3.46 

17 

18 

17.07 

3.43 

17.05 

3.51 

17.04 

3.59 

17.62 

3.66 

18 

19 

18.05 

3.63 

18.63 

3.71 

18.62 

3.79 

18.60 

3.87 

19 

20 

19.03 

3.82 

19.62 

3.90 

19.60 

3.99 

19.58 

4.07 

20 

21 

20.01 

4.01 

20.00 

4.10 

20.58 

4.19 

20.56 

4.28 

21 

22 

21.00 

4.20 

21.58 

4.29 

21.56 

4.39 

21.54 

4.48 

22 

23 

22.58 

4.39 

22.56 

4.49 

22.54 

4.59 

22.52 

4.68 

23 

24 

23.56 

4.58 

23.54 

4.68 

23.52 

4.78 

23.50 

4.89 

24 

25 

24.54 

4.77 

24.52 

4.88 

24.50 

4.9S 

24.48 

5.09 

25 

20 

25.52 

4.96 

25.50 

5.07 

25.48 

5.18 

25.46 

5.30 

26 

27 

20.50 

5.15 

26.48 

5.27 

20.46 

5.38 1 

26.43 

5.50 

27 

28 

27.49 

5.34 

27.46 

5.46 

27.44 

5.58 j 

27.41 

5.70 

28 

29 

28.47 

5.53 

28.44 

5.66 

28.42 

5.78 

28.39 

5.91 

29 

30 

29.45 

5.72 

29.42 

5.85 

29.40 

5.98 

29.37 

6.11 

30 

31 

30.43 

5.92 

30.40 

6.05 

30.38 

6.18 

30.35 

6.31 

31 

32 

31.41 

6.11 

31.39 

6.24 

31.36 

6.38 

31.33 

6.52 

32 

33 

32.39 

6 30 

32.37 

6.44 

32.34 

6.58 

32.31 

6.72 

33 

34 

33.38 

6.49 

33.35 

6.03 

33.32 

6.78 

33.29 

6.92 

34 

35 

34.36 

6.08 

34.33 

6. S3 

34.30 

6.98 

34.27 

7.13 

35 

30 

35.34 

6.87 

35.31 

7.02 

35.28 

7.18 

35.25 

7.33 

36 

37 

36.32 

7.06 

36.29 

7.22 

36.26 

7.38 

36.22 

7.53 

37 

38 

37.30 

7.25 

37.27 

7.41 

37.24 

7.58 

37.20 

7.74 

38 

39 

38.28 

7.44 

38.25 

7.61 

38.22 

7.78 

38.18 

7.94 

39 

40 

39.27 

7.63 

39.23 

7.80 

39.20 

7.97 

39.16 

8.15 

40 

41. 

40.25 

7.82 

40.21 

8.00 

40.18 

8.17 

40.14 

8.35 

41 

42 

41 23 

8.01 

41.19 

8.19 

41.16 

8.37 

41.12 

8.55 

42 

43 

42.21 

8.20 

42.17 

8.39 

42.14 

8.57 

42.10 

8.76 

43 

44 

43.19 

8.40 

43.15 

8.58 

43.12 

8.77 

43.08 

8.96 

44 

45 

44.17 

8.59 

44.14 

8.78 

44.10 

8.97 

44.06 

9.16 

45 

40 

45.15 

8.78 

45.12 

8.97 

45.08 

9.17 

45.04 

9.37 

46 

47 

46.14 

8.97 

46.10 

9.17 

46.06 

9.37 

46.02 

9.57 

47 

48 

47.12 

9.16 

47.08 

9.36 

47.04 

9.57 

46.99 

9.78 

48 

49 

48.10 

9.35 

48.06 

9.5G 

48.02 

9.77 

47.97 

9.98 

49 

50 

49.08 

9.54 

49.04 

9.75 

49.00 

9.97 

48.95 

10.18 

50 

43 

O 

3 

Dep. 

Lat. 

Dep. 

| Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

© 

O 

*—< 

ri 

Ll 

79 Deg. 

78j Deg. 

'H 

Deg. 

78* Deg. 

o 

1 a 

i 









































































































TRAVERSE TABLE 


2 


1 0 

M • 

03 

rf 

P 

3 

o 

0) 

11 Deg. 

lli Dep-. 

i H 

Deg. 

11| Deg. 

Distance. 1 
1 

Lat. 

Dep. 

Lat. 

I/ep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.06 

9.73 

50.02 

9.95 

49.98 

10.17 

49.93 

10.39 

51 

62 

51.04 

9.92 

51.00 

10.14 

50.96 

10.37 

50.91 

10.59 

52 

53 

52.03 

10.11 

5) .98 

10.34 

51.94 

10.57 

51.89 

10.79 

53 

51 

53.01 

10.30 

52.96 

10.53 

52.92 

10.77 

52.87 

11.00 

54 

55 

53.99 

10.49 

53.94 

10.73 

53.90 

10.97 

53.85 

11.20 

55 

56 

54.97 

10.69 

54.92 

10.93 

54.88 

11.16 

54.83 

11.40 

56 

57 

55.95 

10.88 

55.90 

11.12 

55.86 

11.36 

55.81 

11.61 

57 

58 

56.93 

11.07 

56.89 

11.32 

56.84 

11.56 

56.78 

11.81 

58 

59 

57.92 

11.26 

57.87 

11.51 

57.82 

11.76 

57.76 

12.01 

59 

60 

58.90 

11.45 

58.85 

11.71 

58.80 

11.96 

58.74 

12.22 

60 

61 

59.88 

11.64 

59.83 

11.90 

59.78 

12.16 

59.72 

12.42 

61 

62 

60.86 

11.83 

60.SI 

12.10 

60.76 

12.36 

60.70 

12.63 

62 

63 

61.84 

12.02 

61.79 

12.29 

61.74 

12.56 

61.68 

12.83 

63 

64 

62.82 

12.21 

62.77 

12.49 

62.72 

12.76 

62.66 

13.03 

64 

65 

63.81 

12.40 

63.75 

12.68 

63.70 

12.96 

63.64 

13.24 

65 

66 

64.79 

12.59 

64.73 

12.88 

64.68 

13.16 

64.62 

13.44 

66 

67 

65.77 

12.78 

65.71 

13.07 

65.66 

13.36 

65.60 

13.64 

67 

68 

66.75 

12.98 

66.69 

13.27 

66.63 

13.56 

66.58 

13.85 

68 

69 

67.73 

13.17 

67.67 

13.46 

67.61 

13.76 

67.55 

14.05 

69 

70 

68.71 

13.36 

68.66 

13.66 

68.59 

13.96 

68.53 

14.25 

70 

71 

69.70 

13.55 

69.64 

13.85 

69.57 

14.16 

69.51 

14.46 

71 

72 

70.68 

13.74 

70.62 

14.05 

70.55 

14.35 

70.49 

14.66 

72 

73 

71.66 

13.93 

71.60 

14.24 

71.53 

'4.55 

71.47 

14.87 

73 

74 

72.64 

14.12 

72.58 

14.44 

72.51 

14.75 

72.45 

15.07 

74 

75 

73.62 

14.31 

73.56 

14.63 

73.49 

14.95 

73.43 

15.27 

75 

76 

74.60 

14.50 

74.54 

14.83 

74.47 

15.15 

74.41 

15.48 

76 

77 

75.59 

14.69 

75.52 

15.02 

75.45 

15.35 

75 39 

15.68 

77 

78 

76.57 

14.88 

76.50 

15.22 

76.43 

15.55 

76.37 

15.88 

78 

79 

77.55 

15.07 

77.48 

15.41 

77.41 

15.75 

77.34 

16.09 

79 

80 

78.53 

15.26 

78.46 

15.61 

78.39 

15.95 

78.32 

16.29 

80 

81 

79.51 

15.46 

79.44 

15.80 

79.37 

16.15 

79.30 

16.49 

81 1 

82 

80.49 

15.65 

80.42 

16.00 

80.35 

16.35 

80.28 

16.70 

82 B 

83 

81.48 

15.84 

81.41 

16.19 

81.33 

16.55 

81.26 

16.90 

83 1 

84 

82.46 

16.03 

82.39 

16.39 

82.31 

16.75 

82.24 

17.11 

84 

85 

83.44 

16.22 

83.37 

16.58 

83.29 

16.95 

83.22 

17.31 

85 

86 

84.42 

16.41 

84.35 

16.78 

84.27 

17.15 

84.20 

17.51 

86 

87 

85.40 

16.60 

85.33 

16.97 

85.25 

17.35 

85.18 

17.72 

87 

88 

86.38 

16.79 

86.31 

17.17 

86.23 

17.54 

86.16 

17.92 

8S 

89 

87.36 

16.98 

87.29 

17.36 

87.21 

17.74 

87.14 

18.12 

89 

90 

88.35 

17.17 

88.27 

17.56 

88.19 

17.94 

88.11 

18.33 

90 

91 

89.33 

17.36 

89.25 

17.75 

89.17 

18.14 

89.09 

18.53 

91 

92 

90.31 

17.55 

90.23 

17.95 

90.15 

18.34 

90.07 

18.74 

92 

93 

91.29 

17.75 

91.21 

18.14 

91.13 

18.54 

91.05 

18.94 

93 

94 

92.27 

17.94 

92.19 

18.34 

92.11 

18.74 

92.03 

19.14 

94 

95 

93.25 

18.13 

93.17 

18.53 

93.09 

18.94 

93.01 

19.35 

95 

96 

94.24 

18.32 

94.16 

18.73 

94.07 

19.14 

93.99 

19.55 

96 

97 

95.22 

18.51 

95.14 

18.92 

95.05 

19.34 

94.97 

19.75 

97 

98 

96.20 

18.70 

96.12 

19.12 

96.03 

19.54 

95.95 

19.96 

98 

99 

97.18 

18.89 

97.10 

19.31 

97.01 

19.74 

96.93 

20.16 

99 

100 

98.16 

19.08 

98.08 

19.51 

97.99 

19.94 

97.90 

20.36 

100 

« 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

g 

a 

Ci 

*3 

oc 

Q 

79 Deg. 

i 

78$ Deg. 

i 

78| Deg. 

781 Deg. 

+-» 

CO 

• 

Q 





























































































































TRAVERSE TABLE 


*6 


c 

ST 

<-* 

12 Deg 

12J Deg. 

12j 

Deg. 

12| Deg. 

O 
►- • 

CD 

c* 

P 

a 

s 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

0 

CD 

1 

0.98 

0 . 2 T 

0.98 

0.21 

0.98 

0.22 

0.98 

0.22 

1 

2 

1.96 

0.42 

1.95 

0.42 

1.95 

0.43 

1.95 

0.44 

2 

3 

2.93 

0.62 

2.93 

0.64 

2.93 

0.65 

2.93 

0.66 

3 

4 

3.91 

0.83 

3.91 

0.85 

3.91 

0.87 

3.90 

0.88 

4 

5 

4.89 

1.04 

4.89 

1.06 

4.88 

1.08 

4.88 

1.10 

5 

6 

5.87 

1.25 

5.86 

1.27 

5.86 

1.30 

5.85 

I .32 

S 

7 

6.85 

1.46 

6.84 

1.49 

6.83 

1.52 

6.83 

1 54 

7 

8 

7.83 

1.66 

7.82 

1.70 

7.81 

1.73 

7.80 

1 77 

8 

9 

8.80 

1.87 

8.80 

1.91 

8.79 

1.95 

8.78 

1.99 

9 

10 

9.78 

2.08 

9.77 

2.12 

9.76 

2.16 

9.75 

2.21 

10 

11 

10.76 

2.29 

10.75 

2.33 

10.74 

2.38 

10.73 

2.43 

11 

12 

11.74 

2.49 

11.73 

2.55 

11.72 

2.60 

11.70 

2.65 

12 

13 

12.72 

2.70 

12.70 

2.76 

12.69 

2.81 

12.68 

2.87 

13 

14 

13.69 

2.91 

13.68 

2.97 

13.67 

3.03 

13.65 

3.09 

14 

15 

14.67 

3.12 

14.66 

3.18 

14.64 

3.25 

14.63 

3.31 

15 

16 

15.05 

3.33 

15.64 

3.39 

15.62 

3.46 

15.61 

3.53 

16 

17 

16.63 

3.53 

16.61 

3.61 

16.60 

3.68 

16.58 

3.75 

17 

18 

17.61 

3.74 

17.59 

3.82 

17.57 

3.90 

17.56 

3.97 

18 

19 

18.58 

3.95 

18.57 

4.03 

18.55 

4.11 

18.53 

4.19 

19 

20 

19.56 

4.16 

19.54 

4.24 

19.53 

4.33 

19.51 

4.41 

20 

21 

20.54 

4.37 

20.52 

4.46 

20.50 

4.55 

20.48 

4.63 

21 

22 

21.52 

4.57 

21.50 

4.67 

21.48 

4.76 

21.46 

4.86 

22 

23 

22.50 

4.78 

22.48 

4.88 

22.45 

4.98 

22.43 

5.08 

23 

24 

23.48 

4.99 

23.45 

5.09 

23.43 

5.19 

23.41 

5.30 

24 

25 

24.45 

5.20 

24.43 

5.30 

24.41 

5.41 

24.38 

5.52 

25 

26 

25.43 

5.41 

25.41 

5.52 

25.38 

5.63 

25.36 

5.74 

26 

27 

26.41 

5.61 

26.39 

5.73 

26.36 

5.84 

26.33 

5.96 

27 

28 

27.39 

5.82 

27.36 

5.94 

27.34 

6.06 

27.31 

6.18 

28 

29 

28.37 

6.03 

28.34 

6.15 

28.31 

6.28 

28.28 

6.40 

29 

30 

29.34 

6.24 

29.32 

6.37 

29.29 

6.49 

29.26 

6.62 

30 

31 

30.32 

6.45 

30.29 

6.58 

30.27 

6.71 

30.24 

6.84 

31 

32 

31.30 

6.65 

31.27 

6.79 

31.24 

6.93 

31.21 

7.06 

32 

33 

32.28 

6.86 

32.25 

7.00 

32.22 

7.14 

32.19 

7.28 

33 

34 

33.26 

7.07 

33.23 

7.21 

33.19 

7.36 

33.16 

7.50 

34 

35 

34.24 

7.28 

34.20 

7.43 

34.17 

7.58 

34.14 

7.72 

35 

36 

35.21 

7.48 

35.18 

7.64 

35.15 

7.79 

35.11 

7.95 

36 

37 

36.19 

7.69 

36.16 

7.85 

36.12 

8.01 

36.09 

8.17 

37 

38 

37.17 

7.90 

37.13 

8.06 

37.10 

8.22 

37.06 

8.39 

38 

39 

38.15 

8.11 

38.11 

8.27 

38.08 

8.44 

38.04 

8.61 

39 

40 

39.13 

8.32 

39.09 

8.49 

39.05 

8.66 

39.01 

8.83 

40 

41 

40.10 

8.52 

40.07 

8.70 

40.03 

8.87 

39.99 

9.05 

41 

42 

41.08 

8.73 

41.04 

8.91 

41.00 

9.09 

40.96 

9.27 

42 

43 

42.06 

8.94 

42.02 

9.12 

41.98 

9.31 

41.94 

9.49 

43 

44 

43.04 

9.15 

43.00 

9.34 

42.96 

9.52 

42.92 

9.71 

44 

45 

44.02 

9.36 

43.98 

9.55 

43.93 

9.74 

43.89 

9.93 

1 45 

46 

44.99 

9.56 

44.95 

9.76 

44.91 

9.96 

44.87 

10.15 

! 46 

47 

45.97 

9.77 

45.93 

9.97 

45.89 

10.17 

45.84 

10.37 

1 47 ; 

48 

46.95 

9.98 

46.91 

10.18 

48.86 

10.39 

46.82 

10.59 

48 

49 

47.93 

10.19 

47.88 

10.40 

47.84 

10.61 

47.79 

10.81 

49 

5 £ 

48.91 

10.40 

48.86 

10.61 

48.81 

10.82 

48.77 

11.03 

50 

• 

t 

a 

Dep. 

| Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

0 

a 

ctf 

• 00 

t 

78 Deg. 

77| 

Deg. 

77- 

Deg. 

77i Deg. 

1 

.22 

1 0 

1 







































































































traverse table. 


27 


e 

H • 

GO 

pf 

p 

12 Deg. 

12* Deg. 

1 

12T 

Deg. 

12f Deg. 

o 

ST 

p 

a 

O 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

j l 

51 

49.89 

10.60 

49.84 

10.82 

49.79 

11.04 

49.74 

11.20 

51 

52 

50.86 

10.81 

50.82 

11.03 

50.77 

11.25 

50.72 

11.48 

52 

53 

51.84 

11.02 

51.79 

11.25 

51.74 

11.47 

51.69 

11.70 

53 

54 

52.82 

11.23 

52.77 

11.46 

52.72 

11.69 

52.67 

11.92 

54 

55 

53.80 

11.44 

53.75 

11.67 

53.70 

11.90 

53.64 

12.14 

55 

56 

54.78 

11.64 

54.72 

11.88 

54.67 

12.12 

54.62 

12.36 

56 

57 

55.75 

11.85 

55.70 

12.09 

55.65 

12.34 

55.59 

12.58 

57 

58 

56.73 

12.06 

56.68 

12.31 

56.63 

12.55 

56.57 

12.80 

58 

59 

57.71 

12.27 

57.66 

12.52 

57.60 

12.77 

57.55 

13.02 

59 

60 

58.69 

12.47 

58.63 

12.73 

|58.58 

12.99 

58.52 

13.24 

60 

61 

59.67 

12.68 

59.61 

12.94 

59.55 

13.20 

59.50 

13.46 

61 

62 

60.65 

12.89 

60.59 

13.16 

60.53 

13.42 

60.47 

13.68 

62 

63 

61.62 

13.10 

61.57 

13.37 

61.51 

13.64 

61.45 

13.90 

63 

64 

62.60 

13.31 

62.54 

13.58 

62.48 

13.85 

62.42 

14.12 

64 

65 

63.58 

13.51 

63.52 

13.79 

63.46 

14.07 

63.40 

14-35 

65 

66 

64.56 

13.72 

64.50 

14.00 

64.44 

14.29 

64.37 

14.57 

66 

67 

65.54 

13.93 

65.47 

14.22 

65.41 

14.50 

65.35 

14.79 

67 

68 

C6.51 

14.14 

66.45 

14.43 

66.39 

14.72 

66.32 

15.01 

68 

69 

67.49 

14.35 

67.43 

14.64 

67.36 

14.93 

67.30 

15.23 

69 

70 

68.47 

14.55 

68.41 

14.85 

68.34 

15.15 

68.27 

15.45 

70 

71 

69.45 

14.76 

69.38 

15.06 

69.32 

15.37 

69.25 

15.67 

71 

72 

70.43 

14.97 

70.36 

15.28 

70.29 

15.58 

70.22 

15.89 

72 

73 

71.40 

15.18 

71.34 

15.49 

71.27 

15.80 

71.20 

16.11 

73 

74 

72.38 

15.39 

72.32 

15.70 

72.25 

16.02 

72.18 

16,33 

74 

75 

73.36 

15.59 

73.29 

15.91 

73.22 

16.23 

73.15 

16.55 

75 

76 

74.34 

15.80 

74.27 

16.13 

74.20 

16.45 

74.13 

16.77 

76 

77 

75.32 

16.01 

75.25 

16.34 

75.17 

16.67 

75. 10 

16.99 

77 

78 

76.30 

16.22 

1 76.22 

16.55 

76.15 

16.88 

76.08 

17.21 

78 

79 

77.27 

16.43 

77.20 

16.76 

77.13 

17.10 

77.05 

17.44 

79 

80 

78.25 

16.63 

78.18 

16.97 

78.10 

17.32 

78.03 

17.66 

80 

81 

79.23 

16.84 

79.16 

17.19 

79.08 

17.53 

79.00 

17.88 

81 

82 

80.21 

17.05 

80.13 

17.40 

80.06 

17.75 

79.98 

18.10 

82 

83 

81.19 

17.26 

81.11 

17.61 

81.03 

17.96 

80.95 

18.32 

83 

84 

82.16 

17.46 

82.09 

17.82 

82.01 

18.18 

81.93 

18.54 

84 

85 

83.14 

17.67 

83.06 

IS 04 

82.99 

18.40 

82.90 

18.76 

85 

86 

84.12 

17.88 

84.04 

18.25 

83.96 

18.61 

83.88 

18.98 

86 

87 

85.10 

18.09 

85.02 

18.46 

84 .94 

18.83 

84.85 

19.20 

87 

88 

86.08 

18.30 

86.00 

18.67 

85.91 j 

19.05 

85.83 

19.42 

88 

89 

87.06 

18.50 

86.97 

18.88 

86.89 

19.26 

86.81 

19.64 

89 

90 

88.03 

18.71 

87.95 

19.10 

87.871 

19.48 

87.78 

19.86 

90 

91 

89.01 

18.92 

88.93 

19.31 

88.84 

19.70 

80.76 

20.08 

PI 

92 

89.99 

19.13 

89.91 

19.52 

89.82 

19.91 

89. 72 

20.30 

92 

93 

90.97 

19.34 

90.88 

19.73 

90.80 

20.13 

90.71 

29.52 

93 

94 

91.95 

19.54 

91.86 

19.94 

91.77 

20.35 

91.68 

20.75 

94 

95 

92.92 

19.75 

92.84 

20.16 

92.75 

20.56 

92.66 

20.97 1 

95 

96 

93.90 

19.96 

93.81 

20.37 

93.72 

20.78 

93.63 

21.19 | 

96 

97 

94.88 

20.17 

94.79 

20.58 

94.70 

20.99 

94 .61 

21.41 

97 

98 

95.86 

20.38 

95.77 

20.79 

95.68 

21.21 

95.58 

21.63 ! 

98 

99 

96.84 

20.58 

96.75 

21.01 

96.65 

21.43 

96.56 

21.85 

99 

100 

97.81 

20.79 

97.72 

21.22 

97.63 

21.64 

97.53 

22.07 

100 

• 

<u 

o 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

« 

o 

c 

ri 

w 

a 

78 Deg. 

77| Deg 

77 j Deg. 

77* Deg. 

i/3 

• 

Q 




































































































2b 


TRAVERSE TABLE 


Distance 

l 

13 Deg. 

134 Deg. 

m Deg. 

I3.f Deg. 

Distance. 

Lilt. | 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

l 

0.97 

0.23 

0.97 

0.23 

0.97 

0.23 

0.97 

0.24 


2 

1.95 

0.45 

1.95 

0.46 

1.95 

0.47 

1.94 

0.48 

2 

■1 

2 92 

0.67 

2.92 

0.69 

2.92 

0.70 

2.91 

0.71 

3 

4 

3.90 

0.90 

3.89 

0.92 

3.89 

0.93 

3.89 

0.95 

4 

5 

4.87 

1.12! 

4.87 

1.15 

4.86 

1.17 

4.86 

1.19 

5 

6 

5.85 

1.35 

5.84 

1.38 

5.83 

1.40 

5.83 

1.43 

6 

7 

G .82 

1.57 

C.81 

1.60 

6.81 

1.63 

6.80 

1.66 

7 

Si 

7.80 

1.80 

7.79 

1.83 

7.78 

1.87 

7.77 

1.90 

8 

y 

8.77 

2.02 

8.76 

2.06 

8.75 

2.10 

8.74 

2.14 

9 

10 

9.74 

2.25 

9.73 

2.29 

9.72 

2.33 

9.71 

2.38 

10 

li 

0.72 

2.47 

10.71 

2.52 

10.70 

2.57 

10.68 

2.61 

11 

12 

11.69 

2.70 

11.68 

2.75 

11.67 

2.80 

11.66 

2.85 

12 

13 

i2.67 

2.92 

12.65 

2.98 

12.64 

3.03 

12.63 

3.09 

13 

14 

i3.64 

3.15 i 

13.63 

3.21 

13.61 

3.27 

13.60 

3.33 

14 

15 

>4.62 

3.37 

14.60 

3.44 

14.59 

3.50 

14.57 

3.57 

15 

16 

i5.59 

3.00 

15.57 

3.67 

15.56 

3.74 

15.54 

3.80 

16 

17 

;6.57 

3.82 

16.55 

3.90 

16.53 

3.97 

16.51 

4.04 

17 

18 

17.54 

4.05 

17.52 

4.13 

17.50 

4.20 

17.48 

4.28 

18 

19 

18.51 

4.27 

18.49 

4.35 

18.48 

4.44 

18.46 

4.52 

19 

20 

19.49 

4.50 

19.47 

4.58 

19.45 

4.67 1 

19.43 

4.75 

20 

21 

20.46 

4.72 

20.44 

4.81 

20.42 

4.90 

20.40 

4.99 

21 

r* o 

21.44 

4.95 

21.41 

5.04 

21.39 

5.14 

21.37 

5.23 

22 

23 

22.41 

5.17 

22.39 

5.27 

22.36 

5.37 

22.34 

5.47 

23 

24 

23.38 

5.40 

23.36 

5.50 

23.34 

5.60 

23.31 

5.70 

24 

25 

24.36 

5.62 

24.33 

5.73 

24.31 

5.84 

24.28 

5.94 

25 

26 

25.33 

5.85 

25.31 

5.96 

25.28 

6.07 

25.25 

6.18 

26 

27 

26.31 

6.07 

26.28 

6.19 

26.25 

6.30 

26.23 

6.42 

27 

28 

27.28 

6.30 

27.25 

6.42 

27.23 

6.54 

27.20 

6.66 

28 

29 

23.26 

6.52 

28.23 

6.65 

28.20 

6.77 

28.17 

6.89 

29 

30 

29.23 

6.75 

29.20 

6.88 

29.17 

7.00 

29.14 

7.13 

30 

31 

30.21 

6.97 

30.17 

7.11 

30.14 

7.24 

30.11 

7.37 

31 

32 

31.18 

7.20 

31.15 

7.33 

31.12 

7.47 

31.08 

7.61 

32 

33 

32.15 

7.42 

32.12 

7.56 

32.09 

7.70 

32.05 

7.84 

33 

34 

33.13 

7.65 

33.09 

7.79 

33.06 

7.94 

33,03 

8.08 

34 

35 

34.10 

7.87 

34.07 

8.02 

34.03 

8.17 

34.00 

8.32 

35 

36 

35.08 

8.10 

35.04 

8.25 

35.01 

8.40 

34.97 

8.56 

36 

37 

36.05 

8.32 

36.02 

8.48 

35.98 

8.64 

35.94 

8.79 

37 

38 

37.03 

8.55 

36.99 

8.71 

36.95 

8.87 

36.91 

9.03 

38 

39 

38.00 

8.77 

37.96 

8.94 

37.92 

9.10 

37.88 

9.27 

39 

40 

38.97 

9.00 

38.94 

9.17 

38.89 

9.34 

38.85 

9.51 

40 

41 

39.95 

9.22 

39.91 

9.40 

39.87 

9.57 

39.83 

9.75 

41 

42 

40.92 

9.45 

40.88 

9.63 

40.84 

9.80 

40.80 

9.98 

42 

43 

41.90 

9 67 

41.86 

9.86 

41.81 

10.04 

41.77 

10.22 

42 

44 

42.87 

9.90 

42.83 

19.03 

42.78 

10.27 

42.74 

10.16 

44 

45 

43.85 

10.12 

43.80 

10.31 

43.76 

10.51 

43.71 

10.70 

45 

46 

44.82 

10.35 

44.78 

10.54 

44.73 

10.74 

44.68 

10.93 

46 

17 

45.80 

10.57 

45.75 

10.77 

45.70 

10.97 

45.65 

11.17 

47 

48 

46.77 

10.80 

46.72 

11.00 

46.67 

11.21 

46.62 

11.41 

48 

49 

47.74 

11.02 

47.70 

11.23 

47.65 

1 11.41 

47.60 

11.65 

49 

50 

48.72 

11.25 

48.67 

11.46 

48.62 

11.67 

48.57 

| 11.88 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lut. 

i 

Distance.' 

77 Deg. 

76J Deg. 

76-' 

Deg. 

76} Deg. 






































































































TRAVERSE TABLE 


29 


r— 

c 

C/3* 

r** 

P 

3 

n 

a 

13 Deg 

13i Deg. 

13 2 

Deg. 

13| Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

49.69 

11.47 

49.64 

11.69 

49.59 

11.91 

49.54 

12.12 

51 

52 

50.67 

11.70 

50.62 

11.92 

50.56 

12.14 

50.51 

12.36 

52 

53 

51.64 

11.92 

51.59 

12.15 

51.54 

12.37 

51.48 

12.60 

53 

54 

52.62 

12.15 

52.56 

12.38 

52.51 

12.61 

52.45 

12.84 

54 

55 

53.59 

12.37 

53.54 

12.61 

53.48 

12.84 

53.42 

13.07 

55 

56 

54.56 

12.60 

54.51 

12.84 

54.45 

13.07 

54.40 

13.31 

56 

57 

55.54 

12.82 

55.48 

13.06 

55.43 

13.31 

55.37 

13.55 

57 

58 

56.51 

13.05 

56.46 

13.29 

56.40 

13.54 

56 34 

13.79 

58 

59 

57.49 

13.27 

57.43 

13.52 

57.37 

13.77 

57.31 

14.02 

59 

60 

58.46 

13.50 

58.40 

13.75 

58.34 

14.01 

58.28 

14.26 

60 

61 

59.44 

13.72 

59.38 

13.98 

59.31 

14.24 

59.25 

14.50 

61 

62 

60.41 

13.95 

60.35 

14.21 

60.29 

14.47 

60.22 

14.74 

62 

63 

61.39 

14.17 

61.32 

14.44 

61.26 

14.71 

61.19 

14.97 

63 

64 

62.36 

14.40 

62.30 

14.67 

62.23 

14.94 

62.17 

15.21 

64 

65 

63.33 

14.62 

63.27 

14.90 

63.20 

15.17 

63.14 

15.45 

65 

66 

64.31 

14.85 

G4.24 

15.13 

64.18 

15.41 

61.11 

15.69 

66 

67 

65.28 

15.07 

65.22 

15.36 

65.15 

15.64 

65.08 

15.93 

67 

68 

66.26 

15.30 

66.19 

15.59 

66.12 

15.87 

66.05 

16.16 

68 

69 

07.23 

15.52 

67.10 

15.81 

67.09 

16.11 

67.02 

16.40 

69 

70 

68.21 

15.75 

68.14 

16.04 

68.07 

16.34 

67.99 

16.64 

70 

71 

69.18 

15.97 

69.11 

16.27 

69.04 

16.57 

68.97 

10.88 

71 

72 

70.15 

16.20 

70.08 

16.50 

70.01 

16.81 

69.94 

17. 11 

72 

73 

71.13 

16.42 

71.06 

16.73 

70.98 

17.04 

70.91 

17.35 

73 

74 

72.10 

16.65 

72.03 

16.96 

71.96 

17.28 

71.88 

17.59 

74 

75 

73.08 

16.87 

73.00 

17.19 

72.93 

17.50 

72.85 

17.83 

75 

76 

74.05 

17.10 

73.98 

17.42 

73.90 

17.74 

73.82 

18.06 

76 

77 

75.03 

17.32 

74.95 

17.65 

74.87 

17.98 

74.79 

18.30 

77 

78 

76.00 

17.55 

75.92 

17.88 

75.84 

18.21 

75.76 

18.54 

78 

79 

76.98 

17.77 

76.90 

18.11 

76.82 

18.44 

76.74 

18.78 

79 

80 

77.95 

18.00 

77.87 

18.34 1 

77.79 

18.68 

77.71 

19.01 

80 

81 

78.92 

18.22 

78.84 

18.57 J 

78.76 

18.91 

78.68 

19.25 

81 

82 

79.90 

18.45 

79.82 

18.79 

79.73 

19.14 

79.65 

19.49 

82 

83 

80.87 

18.67 

80.79 

19.02 1 

80.71 

19.38 

80.62 

19.73 

83 

84 

81.85 

18.90 

81.76 

19.25 

81.68 

19.61 

81.59 

19.97 

84 

85 

82.82 

19.12 

82.74 

19.48 

82.65 

19.84 

82.56 

20.20 

85 

86 

83.80 

19.35 

83.71 

19.71 

83.62 

20.08 

83.54 

20.44 

86 

87 

84.77 

19.57 

84.68 

19.94 

84.60 

20.31 

84.51 

20.68 

87 

88 

85.74 

19.80 

85.66 

20.17 

85.57 

20.54 

85.48 

20.92 

88 

89 

86.72 

20.02 

86.63 

20.40 

86.54 

20.78 

86.45 

21.15 

89 

90 

87.69 

20.25 

87.60 

20.63 

87.51 

21.01 

87.42 

21.39 

90 

91 

88.67 

20.47 

88.58" 

20.86 

88.49 

21.24 

88.39 

21.63 

91 

92 

89.64 

20.70 

89.55 

21.09 

89.46 

21.48 

89.36 

21.87 

92 

93 

90.62 

20.92 

90.52 

2’ 32 

90.43 

21.71 

90.33 

22.10 

93 

94 

91.59 

21.15 

91.50 

21.54 

91.40 

21.94 

91.31 

22.34 

94 

95 

92.57 

21.37 

92.47 

21.77 

92.38 

22. 18 

92.28 

22.58 

95 

96 

93.54 

21.60 

93.44 

22.00 j 

93.35 

22.41 

93.25 

22.82 

96 

97 

94.51 

21.82 

94.42 

22.23 

94.32 

22.64 

94.22 

23.06 

97 

98 

95.49 

22.05 

95.39 

22.46 

95.29 

22.88 

95.19 

23.29 

98 

99 

96.46 

22.27 

96.36 

22.69 

96.26 

23.11 

96.16 

23.53 

99 

100 

97.44 

22.50 

97.34 

22.92 : 

97.24 

23.34 

97.13 

23 77 

100 

© 

O 

c 

Dep. 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

U 

ri 

CO 

* »"H 

a 

77 Deg. 

76| Deg. 

• 

76 i Deg. 

761 D*g. 

> 

d 

Q ‘ 


21 
































































































30 


TRAVERSE tarle. 


Distance. 

14 Deg. 

14] Deg. 

14| Deg. 

14| Deg. 

►- • 

U 

r+ 

P 

O 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

I 

0.97 

0.24 

0.97 

0.25 

0.97 

0.25 

0.97 

0.25 

\ 

2 

1.94 

0.48 

1.94 

0.49 

1.94 

0.50 

1.93 

0.51 


3 

2.91 

0.73 

2.91 

0.74 

2.90 

0.75 

2.90 

0.76 

3 

4 

3.88 

0.97 

3.88 

0.98 

3.87 

1.00 

3.87 

1.02 

4 

5 

4.85 

1.21 

4.85 

1.23 

4.84 

1.25 

4.84 

1.27 

5 

1 6 

5.82 

1.45 

5.82 

1.48 

5.81 

1.50 

5.80 

1.53 

6 

7 

6.79 

1.69 

6.78 

1,72 

6.78 

1 .75 

6.77 

1.78 

7 

8 . 

7.76 

1.94 

7.75 

1.97 

7.75 

2.00 

7.74 

2.04 

8 

9 

8.73 

2.18 

8.72 

2.22 

8.71 

2.25 

8.70 

2.29 

9 

10 

9.70 

2.42 

9.69 

2.46 

9.68 

2.50 

9.67 

2.55 

10 

11 

10.67 

2.66 

10.66 

2.71 

10.65 

2.75 

10.64 

2.80 

11 

12 

11.64 

2.90 

11.63 

2.95 

11.62 

3.00 

11.60 

3.06 

12 

13 

12.61 

3.15 

12.60 

3.20 

12.59 

3.25 

12.57 

3.31 

13 

14 

13.58 

3.39 

13.57 

3.45 

13.55 

3.51 

13.54 

3.56 

14 

15 

14.55 

3.63 

14.54 

3.69 

14.52 

3.76 

14.51 

3.82 

15 

16 

15.52 

3.87 

15.51 

3.94 

15.49 

4.01 

15.47 

4.07 

16 

17 

16.50 

4.11 

16.48 

4.18 

16.46 

4.26 

16.44 

4.33 

17 

18 

17.47 

4.35 

17.45 

4.43 

17.43 

4.51 

17.41 

4.58 

18 

19 

18.44 

4.60 

18.42 

4.68 

18.39 

4.76 

18.37 

4.84 

19 

20 

19.41 

4.84 

19.38 

4.92 

19.36 

5.01 

19.34 

5.09 

20 

21 

20.38 

5.08 

20.35 

5.17 

20.33 

5.26 

20.31 

5.35 

21 

22 

21.35 

5.32 

21.32 

5.42 

21.30 

5.51 

21.28 

5.60 

22 

23 

22.32 

5.56 

22.29 

5.66 

22.27 

5.76 

‘>9 94. 

5.88 

23 

24 

23.99 

5.91 

|23.26 

5.91 

23.24 

6.01 

23.21 

6.11 

24 

25 

24.28 

6.05 

24.23 

6.15 

24.20 

6.26 

24.18 

6.37 

25 

26 

25.23 

6.29 

25.20 

6.40 

25.17 

6.51 

25.14 

6.62 

26 

27 

26.20 

6.53 

26.17 

6.65 

26.14 

6.76 

26.11 

6.87 

27 

28 

27.17 

6.77 

27.14 

6.89 

27.11 

7.01 

27.08 

7.13 

23 

29 

28.14 

7.02 

28.11 

7.14 

28.08 

7.26 

28.04 

7.33 

29 

30 

29.11 

7.26 

29.08 

7.38 

29.04 

7.51 

29.01 

7.64 

30 

31 

30.08 

7.50 

30.05 

7.63 

30.01 

7.76 

29.93 

7.89 

31 

32 

31.05 

7.74 

31.02 

7.88 

30.98 

8.01 

30.95 

8.15 

32 

33 

32.02 

7.98 

31.98 

8.12 

31.95 

8.26 

31.91 

8.40 

33 

34 

32.99 

8.23 

32.95 

8.37 

Q9 Q9 

8.51 

32.83 

8.60 

34 

35 

33.96 

8.47 

33.92 

8.62 

33.89 

8.76 

33.85 

8.91 

35 

36 

34.93 

8.71 

34.89 

| 8.86 

34.85 

9.01 

34.81 

9.17 

36 

37 

35.90 

8.95 

35.86 

9.11 

35.82 

9.26 

35.78 

9.42 

37 

39 

36.87 

9.19 

36.83 

9.35 

36.79 

9.51 

36.75 

9.67 

38 

39 

37.84 

9.44 

37.80 

9.60 

37.76 

9.76 

37.71 

9.93 

39 

40 

38.81 

9.68 

38.77 

9.85 

38.73 

10.02 

33.68 

10.18 

40 

41 

39.78 

9.92 

39.74 

10.09 

39.69 

10.27 

39.65 

10.44 

41 

42 

40.75 

10.16 

40.71 

10.34 

40.66 

10.52 

40.62 

10.69 

42 

43 

41.72 

110.40 

41.68 

10.58 

41.63 

10.77 

41.58 

10.95 

43 

44 

42.69 

10.64 

42.65 

10.83 

42.60 

11.02 

42.55 

11.20 

44 

45 

43.66 

10.89 

43.62 

11.08 

43.57 

11.27 

43.52 

11.46 

45 

46 

44.63 

11.13 

44.58 

11.32 

44.53 

11.52 

44.48 

11.71 

46 

47 

45.60 

11.37 

45.55 

11.57 

45.50 

11.77 

45.45 

11.97 

47 

48 

46.57 

11.61 

46.52 

11.82 

46.47 

12.02 

46.42 

12.22 

43 

49 

47.54 

11.85 

47.49 

12.06 

47.44 

12.27 

47.39 

12 .43 

49 

50 

48.51 

12.10 

48.46 

12.31 

48.41 

12.52 

48.35 

12 73 

50 

1 Distance.] 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

j Dep. 

i Lat. 

1 

• 

f Distance.| 

76 Deg. 

75] Deg. 

751 Deg. 

75] Deg. 

1 





















































































































VKA.VEKSE TABLE 


31 


Dista 

14 Deg. 

14* Deg. 

14i Deg. 

14* Deg. 

a 

• 

w 

p 

' w 

o 

Lilt. 

Dep. 

Lat« 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

» 

o 

p 

1 fil 

49.49 

12.34 

49.43 

12.55 

49.38 

12.7? 

49.32 

12.98 

51 

52 

50.46 

12.58 

50.40 

12.80 

50.34 

13.02 

50.29 

13.24 

52 

53 

51.43 

12.82 

51.37 

13.05 

51.31 

13.27 

51.25 

13.49 

53 

1 54 

52.40 

13.06 

52.34 

13.29 

52.28 

13.52 

52.22 

13.75 

54 

55 

53.37 

13.31 

53.31 

13.54 

53.25 

13.77 

53.19 

14.00 

55 

! 66 

54.34 

13.55 

54.28 

13.78 

54.22 

14.02 

54.15 

14.26 

56 

5^ 

55.31 

13.79 

55.25 

14.03 

55.18 

14.27 

55.12 

14.51 

57 

, 5S 

56.28 

14.03 

56.22 

14.28 

56.15 

14.52 

56.09 

14.77 

58 

1 59 

57.25 

14.27 

57.18 

14.52 

57.12 

14.77 

57.06 

15.02 

59 

| 60 

58.22 

14.52 

58.15 

14.77 

58.09 

15.02 

58.02 

15.28 

60 

1 61 

59.19 

14.76 

59.12 

15.02 

59.06 

15.27 

58.99 

15.53 

6] 

! 62 

60.16 

15.00 

60.09 

15.26 

60.03 

15.52 

59.96 

15.79 

62 

j 63 

61.13 

15.24 

61.06 

15.51 

60.99 

15.77 

60.92 

16.04 

63 

: 64 

62.10 

15.48 

62.03 

15.75 

61.96 

16.02 

61.89 

16.29 

64 

65 

63.07 

15.72 

63.00 

16.00 

62.93 

16.27 

62.86 

16.55 

65 

i 66 

64.04 

15.97 

63.97 

16.25 

63.90 

16.53 

63.83 

16.80 

66 

\ 67 

65.01 

16.21 

64.94 

16.49 

64.87 

16.78 

64.79 

17.06 

67 

! 68 

65.98 

16.45 

65.91 

16.74 

65.83 

17.03 

65.76 

17.31 

68 

i 69 

66.95 

16.69 

66.88 

16.98 

66.80 

17.28 

66.73 

17.57 

69 

( 70 

67.92 

16.93 

67.85 

17.23 

67.77 

17.53 

67.69 

17.82 

70 

! 71 

68.89 

17.18 

68.82 

17.48 

68.74 

17.78 

68.66 

18.08 

71 

72 

69.86 

17.42 

69.78 

17.72 

69.71 

18.03 

69.63 

18.33 

72 

: 73 

70.83 

17.66 

70.75 

17.9? 

70.67 

18.28 

70.59 

18.59 

73 

! 74 

71.80 

17.90 

71.72 

18.22 

71.64 

18.53 

71.56 

18.84 

74 

75 

72 77 

18.14 

72.69 

18.46 

72.61 

18.78 

72.53 

19.10 

75 

, 76 

73.74 

18.39 

73.66 

18.71 

73.58 

19.03 

73.50 

19.35 

76 

77 

74.71 

18.63 

74.03 

18.95 

74.55 

19.28 

74.46 

19.60 

77 

• 78 

75.08 

18.87 

75.60 

19.20 

75.52 

19.53 

75.43 

19.86 

78 

! 79 

76.05 

19.11 

76.57 

19.45 

76.48 

19.78 

76.40 

20.11 

79 

! 80 

77.62 

19.35 

77.54 

19.69 

77.45 

20.03 

77.36 

20.37 

80 

81 

78.59 

19.60 

78.51 

19.94 

78.42 

20.28 

78.33 

20.62 

81 

* 82 

79.56 

19.84 

79.48 

20.18 

79.39 

20.53 

79.30 

20.88 

82 

■: 83 

80.53 

20.08 

80.45 

20.43 

80.36 

20.78 

80.26 

21.13 

83 

t 84 

81.50 

20.32 

81.42 

20.68 

81.32 

21.03 

81 .23 

21.39 

84 

- 85 

82.48 

20.56 

82.38 

20.92 

82.29 

21.28 

82.20 

21.64 

85 

86 

83.45 

20.81 

83.35 

21.17 

83.26 

21.53 

83.17 

21.90 

86 

87 

84.42 

21.05 

84.32 

21.42 

84.23 

21.78 

84.13 

22.15 

87 

88 

85.39 

21.29 

85.29 

21.66 

85.20 

22.03 

85.10 

22.41 

88 

89 

86.36 

21.53 

86.26 

21.91 

86.17 

22.28 

86.07 

22.66 

89 

90 

87.33 

21.77 

87.23 

22.15 

87.13 

22.53 

87.03 

22.91 

90 

91 

88.30 

22.01 

88.20 

22.40 

88.10 

22.78 

88.00 

23.17 

91 

92 

89.27 

22.26 

89.17 

22.65 

89.07 

23.04 

88.97 

23.42 

92 

93 

90.24 

22.50 

90.14 

22.89 

90.04 

23.29 

89.94 

23.68 

93 

I 94 

91.21 

22.74 

91.11 

23.14 

91.01 

23.54 

90.90 

23.93 

94 

1 95 

92.18 

22.98 

92.08 

23.38 

91.97 

23.79 

91.87 

24.19 

95 

I 96 

93.15 

23.22 

93.05 

23.63 

92.94 

24.04 

92.84 

24.44 

96 

1 97 

94.12 

23.47 

94.02 

23.88 

93.91 

24.29 

93.80 

24.70 

97 

1 98 

95.09 

23.71 

94.98 

24.12 

94.88 

24.54 

94.77 

24.95 

98 

99 

96.06 

23 95 

95.95 

24.37 

95.85 

24.79 

95.74 

25.21 

99 

700 

97.03 

24.19 

96.92 

24.62 

96.81 

25.04 

96.70 

25.46 

100 

© 

o 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

© 

c 

♦-» 

(n 

• 

p 

76 Deg. 

75* Deg 

751 

Deg. 

75* Deg 

(Jj 

Q 




































































































32 


TRAVERS 1 !? TABLE*. 


Distance. 

t 

i 

15 Deg. 

15$ Deg. 


Deg. 

15} Deg. 

V 

o! 

. 

03 . 

r*. \ 

W 

3 

o ; 

» j 

Lat. 

Dep. 

licit* 

Dep^ 

Lst. 

Dep. 

Lat. 

Dep. 

1 

0.97 

0.26 

0.96 

0.26 

0.96 

0.27 

0.96 

0.27 

1 

2 

1.93 

0.52 

1.93 

0.53 

1.93 

0.53 

1.92 

0.54 

2 : 

3 | 

2.90 

0.78 

2.89 

0.79 

2.89 

0.86 

2.89 

0.81 

3 * 

! 4 

3.86 

1.04 

3.86 

1.05 

3.85 

1.07 

3.85 

1.09 

4 1 

2 6 

4.83 

1.29 

4.82 

1.32 

4.82 

1.34 

4.81 

1.36 

5 

6 

5.80 

1.55 

5.79 

1.58 

5.78 

1.60 

5.77 

1.63 

6 ; 

7 

0.76 

1.81 

6.75 

1.84 

6.75 

1.87 

6.74 

1.90 

v 

f 8 

7.73 

2.07 

7.72 

2.10 

7.71 

2.14 

7.70 

2.17 

8 

i 9 

8.69 

2.33 

8.68 

2.37 

8.67 

2.41 

8.66 

2.44 

9 f 

10 

9.66 

2.59 

9.65 

2.63 | 

9.64 

2.67 

9.62 

2.71 

10 

11 

10.63 

2.85 

10.61 

2.89 

10.60 

2.94 

10.59 

2.99 

11 

1 !•» 

11.59 

3.11 

11.58 

3.16 

11.56 

3.21 

11.55 

3.26 

12 

13 

12.56 

3.36 

12.54 

3.42 

12.53 

3.47 

12.51 

3.53 

13 

14 

13.52 

3.62 

13.51 

3.68 

13.49 

3.74 

13.47 

3,80 

14 

15 

14.49 

3.88 

14.47 

3.95 

14.45 

4.01 

14.44 

4.07 

15 

16 

15.45 

4.14 

15.44 

4.21 

15.42 

4.28 

J5.40 

4.34 

16 

17 

16.42 

4.40 

16.40 

4.47 

16.38 

4.54 

16.36 

4.61 

17 

18 

17.39 

4.66 

17.37 

4.73 

17.35 

4.81 

17.32 

4.89 

18 

19 

18.35 

4.92 

18.33 

5.00 

18.31 

5.08 

18.29 

5.16 

19 

20 

19.32 

5.18 

19.30 

5.26 

19.27 

5.34 

19.25 

5.43 

20 

. 21 

20.28 

5.44 

20.26 

5.52 

20.24 

5.61 | 

20.21 

5.70 

21 ; 

22 

21.25 

5.69 

21.23 

5.79 

21.20 

5.88 

21.17 

5.97 

22 

. 23 

22.22 

5.95 

22.19 

6.05 

22.16 

6.15 

22.14 

6.24 

23 

24 

23. 18 

6.21 

23.15 

6.31 

23.13 

6.41 

23.10 

6.51 

24 

25 

24.15 

6.47 

24.12 

6.58 

24.09 

6.68 

24.06 

6.79 

25 

26 

25.11 

6.73 

25.08 

6.84 

25.05 

6.95 

25.02 

7.06 

26 

27 

26.08 

6.99 

26.05 

7.10 

26.02 

7.22 

25.99 

7.33 

27 

28 

27.05 

7.25 

27.01 

7.36 

26.98 

7.48 

20.95 

7.60 

28 

29 

28.01 

7.51 

27.98 

7.63 

27.95 

7.75 

27.91 

7.87 

29 

30 

28.98 

7.76 

28.94 

7.89 

28.91 

8.02 

23.87 

8.14 

30 

31 

29.94 

8.02 

29.91 

8.15 

29.87 

8.28 

29.84 

8.41 

" 31 •: 

32 

30.91 

8.28 

30.87 

8.42 

30.84 

8.55 

30.80 

8.69 

32 

33 

31.88 

8.54 

31.84 

8.68 

31.80 

8.82 

31.76 

8.90 

33 

34 

32.84 

8.80 

32.80 

8.94 

32.76 

9.09 

32.72 

9.23 

84 

35 

33.81 

9.06 

33.77 

9.21 

33.73 

9.35 

33.69 

9.59 

35 . 

36 

34.7 7 

9.32 

34.73 

9.47 

34.69 

9.62 

34.65 

9.77 

36 : 

37 

35.74 

9.58 

35.70 

9.73 

35.65 

9.89 

35.61 

10.04 

37 

38 

36.71 

9.84 

36.66 

10.00 

36.62 

10.16 

36.57 

10.31 

88 

39 

37.67 

10.09 

37.63 

10.26 

37.58 

10.42 

37.54 

10.59 

39 

40 

38.64 

10.35 

38.59 

10.52 

38.55 

10.69 

38.50 

10.86 

40 [ 

41 

39.60 

10.61 

39 . 56 

10.78 

39.51 

10.96 

39.46 

11.13 

11 ; 

42 

:40.57 

10.87 

40 . 52 

11.05 

40.47 

11.22 

40.42 

11 .40 

42 

43 

41.53 

11.13 

41.49 

11.31 

41.44 

11.49 

41.39 

11 .67 

13 

44 

42.50 

11.39 

42.45 

11.57 

42.40 

11.76 

42.35 

11.94 

11 

45 

43.47 

11.65 

43.42 

11.84 

43.36 

12.03 

43.31 

12.21 

45 

16 

44.43 

11.91 

44.38 

12.10 

44.33 

12.29 

LI. 27 

12.49 

46 

47 

:45.40 

12.16 

45.35 

12.36 

45.29 

12.56 

45.24 

12.76 

47 

i 48 

46.36 

12.42 

46.31 

12.63 

46.25 

12.83 

1 46.20 

13.03 

48 

49 

47.33 

12.68 

47.27 

12.89 

47.22 

13.09 

147.16 

13.30 

49 

50 

48.30 

12.94 

48.24 

13.15 

48.18 

13.36 

|48.12 

13.57 

50 

1 

Distance. 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

Lat. 

Dep. 

Lat. 

; 

I Distance. 

* 

75 

Deg. 

74} Deg. 

74*- 

Deg. 

74$ Deg. 























































































































TRAVERSE TABLE. 




o 
»— • 
m 

r-~ 

P 

15 Deg. 

15} Deg 

15£ 

Deg. 

15} Deg. 

i 

> 

W 

CO 

r+- 

3 

n 

CO 

Lat. 

1 Dep. 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lat* 

Dep. 

P 

P > 

O ! 

P 

s 51 

49.26 

13.20 

49.20 

13.41 

49.15 

13.63 

49.09 

13.84 

51 

i 52 

50.23 

13.46 

50.17 

13.68 

50.11 

13.90 

50.05 

14.11 

52’ 

1 53 

51.19 

13.72 

51.13 

13.94 

51.07 

14.16 

51.01 

14.39 

53 

1 54 

52.16 

13.98 

52.10 

14.20 

52.04 

14.43 

51.97 

14.60 

54 

■ 65 

53.13 

14.24 

53.06 

14.47 

53.00 

14.70 

52.94 

14.93 

55 

! 56 

54.09 

14.49 

54.03 

14.73 

53.96 

14.97 

53.90 

15.20 

56 

\ 57 

55.06 

14.75 

54.99 

14.99 

54.93 

15.23 

54.86 

15.47 

57 

S 58 

56.02 

15.01 

55.96 

15.26 

55.89 

15.50 

55.82 

15.74 

58 

59 

56.99 

15.27 

56.92 

15.52 

56.85 

15.77 

56.78 

16.01 

59 

! 60 

57.96 

15.53 

57.89 

15.78 

57.82 

16.03 

57.75 

16.29 

60 

v 61 

58.92 

15.79 

58.85 

16.04 

58.78 

18.30 

58.71 

16.56 

61 

\ 62 

59.89 

16.05 

59.82 

16.31 

59.75 

16.57 

59.67 

16.83 

62 

, 63 

60.85 

16.31 

60.78 

16.57 

60.71 

16.84 

60.63 

17.10 

63 

: 64 

61.82 

16.56 

61.75 

16.83 

61.67 

17.10 

61.60 

17.37 

64 

3 65 

62.79 

16.82 

62.71 

17.10 

62.64 

17.37 

62.56 

17.64 

65 

; 66 

63.75 

17.08 

63.68 

17.35 

63.60 

17.64 

63.52 

17.92 

66 

i 67 

64.72 

17.34 

64.64 

17.62 

64.56 

17.90 

64.48 

18.19 

67 

j 68 

65.68 

17.60 

65.61 

17.89 

65.53 

18.17 

65.45 

18.46 

68 

{ 69 

66.65 

17.86 

66.57 

18.15 

66.49 

18.44 

66.41 

18.73 

69 

' 70 

67.61 

18.12 

67.54 

18.41 

67.45 

18.71 

67.37 

19.00 

70 

i 7i 

68.58 

18.38 

68.50 

18.68 

68.42 

18.97 

68.33 

19.27 

71 

72 

69.55 

18.63 

69.46 

18.94 

69.38 

19.24 

69.30 

19.54 

72 

73 

70.51 

18.89 

70.43 

19.20 

70.35 

19.51 

70.26 

19.82 

73 

1 74 

71.48 

19.15 

71.39 

19.46 

71.31 

19.78 

71.22 

20.09 

74 

75 

72.44 

19.41 

72.36 

19.73 

72.27 

20.04 

72.18 

20.36 

75 

| 76 

73.41 

19.67 

73.32 

19.99 

73.24 

20.31 

73.15 

20.63 

76 

t 77 

74.38 

19.93 

74.29 

20.25 

74.20 

20.58 

74.11 

20.90 

77 

* 78 

75.34 

20.19 

75.25 

20.52 

75.16 

20.84 

75.07 

21.17 

78 

i 79 

76.31 

20.45 

76.22 

20.78 

76.13 

21.11 

76.03 

21.44 

79 

80 

77.27 

20.71 

77.18 

21.04 

77.09 

21.38 

77.00 

21.72 

80 

i 81 

78.24 

20.96 

78.15 

21.31 

78.05 

21.65 

77.96 

21.99 

81 

82 

79.21 

21.22 

79.11 

21.57 

79.02 

21.91 

78.92 

22.26 

82 

l 83 

89. 17 

21.48 

80.08 

21.83 

79.98 

22.18 

79.88 

22.53 

83 

' 84 

81.14 

21.74 

81.04 

22.09 

80.94 

22.45 

80.85 

22.80 

84 

j 85 

82.10 

22.00 

82.01 

22.36 

81 .91 

22.72 

81.81 

23.07 

85 

5 86 

83.07 

22.26 

82.97 

22.62 

82.87 

22.98 

82.77 

23.34 

86 

87 

84.04 

22.52 

83.94 

22.88 

83.84 

23.25 

83.73 

23.62 

87 

88 

85.00 

22.78 

84.90 

23.15 

84.80 

23.52 

84.70 

23.89 

88 

89 

85.97 

23.03 

85.87 

23.41 

85.76 

23.78 

85.66 

24.16 

89 

90 

86.93 

23.29 

86.83 

23.67 

86.73 

24.05 

86.62 

24.43 

90 

! 91 

87.90 

23.55 

87.80 

23.94 

87.69 

24.32 

87.58 

24.70 

91' 

i 92 

88.87 

23.81 

88.76 

24.20 

88.65 

24.59 

88.55 

24.97 

92 

93 

89.83 

24.07 

89.73 

24.46 

89.62 

24.85 

89.51 

25.24 

93 

i 94 

90.80 

24.33 

90.69 

24.72 

90.58 

25.12 

90.47 

25-52 

94 

| S5 

91.76 

24.59 

91.65 

24.99 

91 54 

25.39 

91.43 

25.79 

95 

96 

92 73 

24.85 

92.62 

25.25 

92.51 

25.65 

92.40 

26.06 

96 

! 97 

93.69 

25.11 

93.58 

25.51 

93.47 

25.92 

93.36 

26.33 

97 

98 

94.66 

25.36 

94.55 

25.78 

94.44 

26.19 

94.32 

26.60 

98 

! 99 

95.63 

25.62 

95.51 

26.04 

95.40 

26.46 

95.28 

26.87 

99 

\ 100 

96.59 

25.88 

36.48 

26.30 

96.36 

26.72 

96.25 

27.14 

100 

1 R 

s 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

v i 

O ' 

C 

<§ 

75 Deg. 

74} Deg. 

744 Deg. 

74} Deg. 

03 

♦-> 

UQ • 

• 

O 
































































































4 


TRAVERSE TAB2,2 


j 

o 

M 

tr*- 

JO 

16 Deg. 

16J Deg. 

18i Deg. 

16f Dog. 

© 

r* 

CO 

p9 

3 

n 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

3 

® 

l 

0.96 

0.28 

0.96 

0.28 

0.96 

0 28 

0.96 

0.29 

1 

2 

1 92 

0 55 

1.92 

0.56 

1.92 

0.57 

1.92 

0.58 

2 

3 

2.88 

C 83 

2.88 

0.84 

2.88 

0.85 

2.87 

0.86 

3 

4 

3.85 

1.10 

3.84 

1.12 

3.84 

1.14 

3.83 

1.15 • 

4 

5 

4.81 

1.38 

4.80 

1.40 

4.79 

1.42 

4.79 

1.44 

5 

6 

5.77 

1.65 

5.76 

1.68 

5.75 

1.70 

5.75 

1.73 

6 

7 

6.73 

1.93 

6.72 

1.96 

6.71 

1.99 

6.70 

2.02 

7 

8 

7.69 

2.21 

7.68 

2.24 

7.67 

2.27 

7.66 

2.31 

8 

9 

8.65 

2.48 

8.64 

2.52 

8.63 

2.56 

8.62 

2.59 

9 

10 

9.61 

2.76 

9.60 

2.80 

9.59 

2.84 

1 

9.58 

2.S8 

10 

11 

10.57 

3.03 

10.56 

3.08 

10.55 

3.12 

10.53 

3.17 

11 

12 

11.54 

3.31 

11.52 

3.36 

11.51 

3.41 

11.49 

3.46 

12 

13 

12.50 

3.58 

12.48 

3.64 

12.46 

3.69 

12.45 

3.75 

13 

14 

13.46 

3.86 

13.44 

3.92 

13.42 

3.98 

13.41 

4.03 

14 

15 

14.42 

4.13 

14.40 

4.20 

14.38 

4.26 

14.36 

4.32 

15 

16 

15.38 

4.41 

15.36 

4.48 

15.34 

4.54 

15.32 

4.61 

16 

17 

16.34 

4.69 

16.32 

4.76 

16.30 

4.83 

16.28 

4.90 

17 

18 

17.30 

4.96 

17.28 

5.04 

17.26 

5.11 

17.24 

5.19 

18 

19 

18.26 

5.24 

18.24 

5.32' 

18.22 

5.40 

18.19 

5.48 

19 

20 

19.23 

5.51 

19.20 

5.60 

19.18 

5.68 

19.15 

5.76 

20 

21 

20.19 

5.79 

20.16 

5.88 

20.14 

5.96 

20.11 

6.05 

21 

OO 

** 

21.15 

6.06 

21.12 

6.16 

21.09 

6.25 

21.07 

6.34 

22 

23 

22.11 

6.34 

22.08 

6.44 

22.05 

6.53 

22.02 

6.63 

23 

24 

23.07 

6.62 

23.04 

6.72 

23.01 

6.82 

22.98 

6.92 

24 

25 

24.03 

6.89 

24.00 

7.00 

23.97 

7.10 

23.94 

7.20 

25 

26 

24.99 

7.17 

24.96 

7.28 

24.93 

7.38 

24.90 

7.49 

26 

27 

25.95 

7.44 

25.92 

7.56 

25.89 

7.67 

25.85 

7.78 

27 

28 

26.92 

7.72 

26.88 

7.84 

26.85 

7.95 

26.81 

8.07 

28 

29 

27.88 

7.99 

27.84 

8.11 

27.81 

8.24 

27.77 

8.36 

29 

30 

28.84 

8.27 

28.80 

8.39 

28.76 

8.52 

28.73 

8.65 

30 

31 

29.80 

8.54 

29.76 

8.67 

29.72 

8.80 

29.68 

8.93 

31 

32 

30.76 

8.82 

30.72 

8.95 

30.68 

9.09 

30.64 

9.22 

32 

33 

31.72 

9.10 

31.69 

9.23 

31.64 

9.37 

31.60 

9.51 

33 

34 

32.68 

9.37 

32.64 

9.51 

32.60 

9.66 

32.56 

9.80 

34 

35 

33.64 

9.65 

33.60 

9.79 

33.56 

9.94 

33.51 

10.09 

35 

36 

34.61 

9.92 

34.56 

10.07 

34.52 

10.22 

34.47 

10.38 

36 

37 

35.57 

10.20 

35 52 

10.35 

35.48 

10.51 

35.43 

10.66 

37 

38 

36.53 

10.47 

36.48 

10.63 

36.44 

10.79 

36.39 

10.95 

38 

39 

37.49 

10.75 

37-44 

10.91 

37.39 

11.08 

37.35 

11.24 

39 

40 

38.45 

11.03 

38.40 

11.19 

38.35 

11.36 

38.30 

11.53 

40 

41 

39.41 

11.30 

39.36 

11.47 

39.31 

11 .64 

39.26 

1 1 .82 

41 

42 

40.37 

11.58 

40.32 

11.75 

40.27 

11.93 

40.22 

12.10 

42 

43 

41.33 

11.85 

41.28 

12.03 

41.23 

12.21 

41.18 

12.39 

43 

44 

42.30 

12.13 

42.24 

12.31 

42.19 

12.50 

42.13 

12.68 

1 44 

45 

43.26 

12.40 

43.20 

12.59 

43.15 

12.78 

43.09 

12.97 

45 

46 

44.22 

12.68 

44.16 

12.87 

44.11 

13.06 

44.05 

13.26 

46 

47 

45.18 

12.95 

45.12 

13.15 

45. OG 

13.35 

45.01 

13.55 

47 

48 

46.14 

13.23 

46.08 

13.43 

46.02 

13.63 

45.96 

13.83 

48 

49 

47.10 

13.51 

47.04 

13.71 

46.98 

13.92 

46.92 

14.12 

49 

50 

48.06 

13.78 

48.00 

13.99 

47.91 

14.20 

47.88 

14.41 

50 

d 

o 

** 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

CD 

O 

a 

rt 

4-) 

cn 

° 

74 Dog. 

73J Deg. 

731 

Deg. 

73} Deg. 

CtJ 

.2 

Q 




















































































































TRW ERSE TAJ1LE. 36 


nr 

P 

16 Deg. 

16^ Deg. 

16* 

Deg 

16| Deg. 

c 

00* 

r+ 

p 

3 

o 

© 

Lat. 

Dep. 

Lat. 

Dep. 

L<it* 

Dep. 

Lat. 

Dep. 

b 

o 

© 

5l 

49.02 

14.06 

48.96 

14.27 

48.90 

14.48 

48.84 

14.70 

~K! 

52 

49.99 

14.33 

49.92 

14.55 

49 86 

14.77 

49.79 

14.99 

52 

53 

50.95 

14.61 

50.88 

14 83 

50.82 

15.05 

50.75 

15.27 

53 

54 

51.91 

14.88 

51.84 

15 11 

51.78 

15.34 

51.71 

15.56 

54/ 

55 

52.87 

15.16 

52.80 

15.39 

52.74 

15.62 

52.67 

15.85 

5.1 

56 

53.83 

15.44 

53.76 

15.67 

53.69 

15.90 

53.62 

16.14 

5(1 

57 

54.79 

15.71 

54.72 

15.95 

54.65 

16.19 

54.58 

16.43 

5'. 1 

58 

55.75 

15.99 

55.68 

16.23 

55.61 

16.47 

55.54 

16.72 

58 

59 

56.71 

16.26 

56.64 

16.51 

56.57 

16.76 

56.50 

17.00 

59 

60 

57.68 

16-54 

57.60 

16.79 

57.53 

17.04 

57.45 

17.29 

60 

61 

58.64 

16.81 

58.56 

17.07 

58.49 

17.32 

58.41 

17.58 

61 

62 

59.60 

17.09 

59.52 

17.35 

59.45 

17.61 

59.37 

17.87 

62 

63 

60.56 

17.37 

50 48 

17.63 

60.41 

17.89 

60.33 

18.16 

63 

64 

61.52 

17.64 

61 -44 

17.91 

61.36 

18.18 

61.28 

18.44 

64 

65 

62.48 

17.92 

62.49 

18.19 

62.32 

18.46 

62.24 

18.73 

65 

66 

63.44 

18.19 

63.33 

18.47 

63.28 

18.74 

63.20 

19.02 

66 

67 

64.40 

18.47 

64.32 

18.75 

64.24 

19.03 

64.16 

19.31 

67 

68 

65.37 

18.74 

65.28 

19.03 

65.20 

19.31 

65.11 

19.60 

68 

69 

66.33 

19.02 1 

66.24 

19.31 

66.16 

19.60 

66.07 

19.89 

69 

70 

67.29 

19.29 

67.20 

19.59 

67.12 

19.88 

67.03 

20.17 

70 

71 

68.25 

19.57 

68 . 16 

19.87 

68.08 

20.17 

67.99 

20.46 

71 

72 

69.21 

19.85 

69. 12 

20.15 

69.03 

20.45 

68.95 

20.75 

72 

73 

70.17 

20.12 

70.08 

20.43 

69.99 

20.73 

69.90 

21.04 

73 

74 

71.13 

20.40 

71.04 

20.71 

70.95 

21.02 

70.86 

21.33 

74 

75 

72.09 

20.67 

72.00 

20.99 

71.91 

21.30 

71.82 

21.61 

75 

76 

73.06 

20.95 

72.96 

21.27 

72.87 

21.59 

72.78 

21.90 

76 

77 

74.02 

21.22 

73.92 

21.55 

73.83 

21.87 

73.73 

22.19 

77 

78 

74.98 

21.50 

34.88 

21.83 

74.79 

22.15 

74.69 

22.48 

78 

79 

75.94 

21.78 

75.84 

22.11 

75.75 

22.44 

75.65 

22.77 

79 

80 

76.90 

22.05 

76.80 

22.39 

76.71 

22.72 

76.61 

23.06 

80 

81 

77.80 

22.33 

77.76 

22.67 

77.66 

23.01 

177.56 

23.34 

' 81 

82 

78.82 

22.60 

78.72 

22.95 

78.62 

23.29 

78.52 

23.63 

82 

83 

79.78 

22.88 

79.68 

23.23 

79.58 

23.57 

79.48 

23.92 

83 

84 

80.75 

23.15 

80.64 

23.51 

80.54 

23.86 

80.44 

24.21 

84 

85 

81.71 

23.43 

81.60 

23.79 

81.50 

24.14 

81.39 

24.50 

85 

86 

82.67 

23.70 

82.56 

24.07 

82.46 

24.43 

i82.35 

24.78 

86 

87 

83.63 

23.98 

83.52 

24.35 

83.42 

24.71 

83.31 

25.07 

87 

88 

84.59 

24.26 

84.48 

24.62 

84.38 

24.99 

84.27 

25.36 

88 

89 

85.55 

24.53 

85.44 

24.90 

85.33 

25.28 

85.22 

25.65 

89 

90 

86.51 

24.81 

86.40 

25.18 

86.29 

25.56 

86.18 

25.94 

90 

91 

87.47 

25.08 

87.36 

25.46 

87.25 

25.85 

87.14 

26.23 

91 

92 

88.44 

25.36 

88.32 

25.74 

88.21 

26.13 

|88.10 

26.51 

92 

93 

89.40 

25.63 

89.28 

26.02 

89.17 

26.41 

89.05 

26.80 

93 

94 

90.36 

25.91 

90.24 

26.30 

90.13 

26.70 

90.01 

27.09 

94 

95 

91.32 

26.19 

91.20 

26.58 

91.09 

26.98 

90.97 

27.38 

95 

96 

92.28 

26.46 

92.16 

26.86 

92.05 

27.27 

I 91.93 

27.67 

96 

97 

93.24 

26.74 

93.12 

27.14 

93.01 

27.55 

192.88 

27.95 

97 

98 

94.20 

27.01 

94.08 

27.42 

93.96 

27.83 

93.84 

28.24 

98 

99 

95.16 

27.29 

95.04 

27.70 

94.92 

28.12 

94.80 

28.53 

99 

100 

96.13 

27.56 

96.00 

27.98 

95.88 

28.40 

95.76 

28.82 

2 00 

a> 

o 

a 

Dep. 

licit* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat* 

i 

c 

cd 

or> 

Q 

74 Deg. 

73f Deg. 

73^ 

Deg. 

I 

73! Deg. 

c i 

CO 

• H 

1 c 






















































































































36 


TRAVERSE TABLE. 


o 

H • 

CO 

p 

17 Deg. 

17* Deg. 

Yl\ Deg. ! 

173 Deg. 

C 

• 

GO 

r-+ 

p> 

s i 

o 

® 

• { 

Lat. 

Dep. j 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

ft 

l i 

0.96 

0.29 

0.95 

0.30 

0.95 

0.30 

0.95 

0.30 

1 

2 i 

1.91 

0.58 

1.91 

0.59 

1.91 

0.60 

1.90 

0.61 


3 

2.87 

0.88 

2.87 

0.89 

2.86 

0.90 

2.86 

0.91 

3 

4 

3.83 

1.17 

3.82 

1.19 

3.81 

1.20 

3.81 

1,22 

4 

5 

4.78 

1.46 

4.78 

1.48 

4.77 

1.50 

4.76 

1.52 

5 

.*• 6 

5.74 

1.75 

5.73 

1.78 

5.72 

1.80 

5.71 

1.83 

6 

• 7 

6.69 

2.05 

6.69 

2.08 

6.68 

2.10 

6.67 

2 13 

1 

8 

7.65 

2.34 

7.64 

2.37 

7.63 

2.41 

7.62 

2.44 

9 

9 

8.61 

2.63 

8.60 

2.67 

8.58 

2.71 

8 57 

2.74 

9 

10 

9.56 

2.92 

9.55 

2.97 

9.54 

3.01 

9.52 

3.05 

10 

11 

10.52 

3.22 

10.51 

3.26 

10.49 

3.31 

10.48 

3.35 

11 

12 

11.48 

3.51 

11.45 

3.56 

11.44 

3.61 

11.43 

3.66 

12 

13 

12.43 

3.80 

12.42 

3.85 

12.40 

3. 91 

12.38 

3.96 

13 

14 

13.39 

4.09 

13.37 

4.15 

13.35 

4.21 

13.33 

4.27 

14 

15 

14.34 

4.39 

14.33 

4.45 

14.31 

4.51 

14.29 

4.57 

15 

16 

15.30 

4.68 

15.28 

4.74 

15.26 

4.81 

15.24 

4.88 

16 

17 

16.26 

4.97 

16.24 

5.04 

16.21 

5.11 

16. 19 

5.18 

17 

18 

17.21 

5.26 

17.19 

5.34 

17.17 

5.41 

17. 14 

5.49 

IS 

19 

18.17 

5.56 

18.15 

5 63 I 

18.12 

5.71 

18.10 

5.79 

19 

20 

19.13 

5.85 

19.10 

5. 93 | 

19.07 

6.01 

19.05 

6.10 

20 

21 

20.08 

6.14 

20.06 

6.23 ! 

20.03 

6.31 

20.00 

6.40 

21 

22 

21.04 

6.43 

21.01 

G 52 | 

20.98 

6.62 

20.95 

6.71 

22 

23 

21.99 

6.72 

21.97 

6.82 

21.94 

6.92 

21.91 

7.01 

23 

24 

22.95 

7.02 

22.92 

7.12 

22.89 

7.22 

22.86 

7.32 

24 

25 

23.91 

7.31 

23.89 

7 41 

23.84 

7.52 

23.81 

7.62 

25 

26 

24.86 

7.60 

24.83 

7.71 

24.80 

7.82 

24.76 

7.93 

26 

27 

25.82 

7.89 

25.79 

8.01 

25.75 

8.12 

25.71 

8.23 

27 

28 

26.78 

8.19 

26.74 

8.30 

26.70 

8.42 

26.67 

8.54 

28 

29 

27.73 

8.48 

27.70 

8.60 

27.66 

8.72 

27.62 

8.84 

29 

30 

28.69 

8.77 

29.65 

8.90 

28.61 

9.02 

28.57 

9.15 

30 

31 

29.65 

9.06 

29.61 

9.19 

29.57 

9.32 

29.52 

9.45 

31 

32 

30.60 

9.36 

30.56 

9.49 

30.52 

9.62 

30.48 

9.76 

32 

33 

31 .56 

9.65 

31.52 

9.79 

31.47 

9.92 

31.43 

10.06 

33 

34 

32.51 

9.94 

32.47 

10.08 

32.43 

10.22 

32.38 

10.37 

34 

35 

83.47 

10.23 

33.43 

10.38 

33.38 

10.52 

33.33 

10.67 

35 

36 

34.43 

10.53 

34.38 

10.68 

34.33 

10.83 

34.29 

10.98 

36 

37 

35.38 

10.82 

35.34 

10.97 

35.29 

11.13 

35 24 

11.28 

37 

38 

36.34 

11.11 

36.29 

11.27 

36.24 

11.43 

36.19 

11.58 

38 

39 

37.30 

11.40 

37.25 

11.57 

37.19 

11.73 

37.14 

11.89 

39 

40 

38.25 

11.69 

38.20 

11.86 

38.15 

12.03 

38.10 

12.19 

40 

41 

39.21 

11.99 

39.16 

12.16 

39.10 

12.33 

39.05 

12.50 

41 

1 42 

40.16 

12.28 

40.11 

12.45 

40.06 

12.63 

40.00 

12.80 

42 

1 43 

41.12 

12.57 

41.07 

12.75 

41.01 

12.93 

40.95 

13.11 

43 

I 44 

42.08 

12.86 

42.02 

13.05 

41.96 

13.23 

41.91 

13.41 

44 

■ 45 

43.03 

13.16 

42.98 

13.34 

42.92 

13.53 

42.86 

13.72 

45 

\ 46 

43.99 

13.45 

43.93 

13.64 

43.87 

13.83 

43.81 

14.02 

46 

•| 47 

44.95 

13.74 

44.89 

13.94 

44.82 

14.13 

44.76 

14.33 

47 

' 48 

45.90 

14.03 

45.84 

14.23 

45.78 

14.43 

45.71 

14 63 

48 

49 

46.86 

14.33 

46.80 

14.53 

46.73 

14.73 

46.67 

14.94 

49 

50 

47.82 

14.62 

47.75 

14.83 

47.69 

15.04 

47.62 

15.24 

50 

8 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<u 

o 

■c 

cJ 

.2 

O 

73 Deg. 

I 

72f Deg. 

72| 

Deg. 

72* Deg. 

+-> 

CO 

Q 






























































































































TRAVERSE table 


37 


O 

ST 

p 

17 Deg. 

17} Deg. 

nj 

Deg. 

m Deg. 

G 
►— • 
to 
«-► 

P 

» 

o 

® 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

3 

‘ 51 

48.77 

14.91 

48.71 

15.12 

48.64 

15.34 

48.57 

15.55 

51 

52 

49.73 

15.20 

49.66 

15.42 

49.59 

15.64 

49.52 

16.85 

52 

53 

50.68 

15.50 

50.62 

15.72 

50.55 

15.94 

50.48 

16. 16 

53 

54 

51.64 

15.79 

51.57 

16.01 

51.50 

16.24 

51.43 

16.46 

54 

55 

52.60 

16.08 

52.53 

16.31 

52.45 

16.54 

52.38 

16.7? 

55 

56 

53.55 

16.37 

53.48 

16.61 

53.41 

16.84 

53.33 

17.07 

56 

57 

54.51 

16.67 

54.44 

16.90 

54.36 

17.14 

54.29 

17.33 

57 

58 

55.47 

16.96 

55.39 

17.20 

55.32 

17.44 

55.24 

17.68 

58 

59 

56.42 

17.25 

56.35 

17.50 

56.27 

17.74 

56.10 

17.99 

59 

60 

57.38 

17.54 

57.30 

17.79 

57.22 

18.04 

57.14 

18.29 

60 

61 

58.33 

17.83 

58.26 

18.09 

58.18 

18.34 

58.10 

18.60 

61 

62 

59.29 

18.13 

59.21 

18.39 

59.13 

18.64 

59.05 

13.90 

62 

63 

60.25 

18.42 

60.17 

18.68 

60.08 

18.94 

60.00 

19.21 

6.3 

64 

61.20 

18.71 

61.12 

18.98 

61.04 

19.25 

60.95 

19.51 

64 

65 

62.16 

19.00 

62.08 

19.28 

61.99 

19.55 

61.91 

19.82 

65 

66 

63.12 

19.30 

63.03 

19.57 

62.95 

19.35 

62.86 

20 . 12 

66 

67 

64.07 

19.59 

63.99 

19.87 

63.90 

20.15 

63.81 

20.43 

67 

68 

65.03 

19.88 

04.94 

20.16 

64.85 

20.45 

64.76 

20.73 

68 

69 

65.99 

20.17 

65.90 

20.46 

65.81 

20. 75 

65.72 

21.04 

69 

70 

66.94 

20.47 

66.85 

20.76 

66.76 

21.05 

66.67 

21.34 

70 

71 

67.90 

20.76 | 

67.81 

21.05 

67.71 

21.35 

67.62 

21 .65 

71 

72 

68.85 

21.05 i 

68.76 

21.35 

68.67 

21.65 

68 .57 

21.95 

72 

73 

69.81 

21.34| 

69.72 

21.65 

69.62 

21.95 

69.52 

22.26 

73 

74 

70.77 

21.64 

70.67 

21.94 

|70.58 

22.25 j 

70.48 

22.56 

74 

75 

71.72 

21.93 

71.63 

22.24 

j71.53 

22.55 1 

71.43 

22.86 

75 

76 

72.68 

22.22 

72.58 

22.54 

72.48 

22.85 

72.38 

23.17 

76 

77 

73.64 

22.51 

73.54 

22.83 

73.44 

23.15 

73.33 

23.47 

77 

78 

74.59 

22.80 

74.49 

23.13 

74.39 

23.46 

74.29 

23.78 

78 

79 

75.55 

23.10 

75.45 

23.43 

75.34 

23.76 

75.24 

24.08 

79 

80 

76.50 

23.39 

70.40 

23.72 

76.30 

24.06 

76.19 

24.39 

80 

81 

77.46 

23.68 

77.36 

24.02 

77.25 

24.36 

77.14 

24.69 

81 

92 

78.42 

23.97 

78.31 

24.32 

78.20 

24.66 

78.10 

25.00 

82 

83 

79.37 

24.27 

79.27 

24.61 ! 

79.16 

25.96 

79.05 

25.30 

83 

84 

80.33 

24.56 

80.22 

24.91 j 

80.11 

25.26 

80.00 

25.61 

84 

85 

81.29 

24.85 

81.18 

25.21 

81.07 

25.56 

80.95 

25.91 

85 

86 

82.24 

25.14 

82. 13 

25.50 

82.02 

25.86 

81.91 

26.22 

86 

87 

83.20 

25.44 

83.09 

25.80 

82.97 

26.16 

82.86 

26.52 

87 

88 

84.15 

25.73 

84.04 

26.10 

83.93 

26.46 

83.81 

26.83 

88 

89 

85.11 

26.02 

85.00 

26.39 

84.88 

26.76 

84.76 

27.13 

89 

90 

86.07 

26.31 

85.95 

26.69 

85.83 

27.06 

85.72 

27.44 

90 

91 

87.02 

26.61 

86.91 

26.99 

86.79 

27.36 

86.67 

27.74 

91 

92 

87 98 

26.90 

87.86 

27.28 

87.74 

27.66 

87.62 

28.05 

92 

93 

88.94 

27.19 

88.82 

27.58 

88.70 

27.97 

88.57 

28.35 

93 

94 

89.89 

27.48 

89.77 

27.87 

89.65 

28.27 

89.53 

28.66 

94 

95 

90.85 

27.78 

90.73 

28.17 

90.60 

28.57 

90.48 

28.96 

95 

96 

91 8! 

28.07 

91.68 

28.47 

91.56 

28.87 

91.43 

29.27 

96 

97 

92.7* 

28.36 

92.64 

28.76 

92.51 

29.17 

92.38 

29.57 

97 

98 

93.72 

28.65 

93.59 

29.06 

93.46 

29.47 

93.33 

29.88 

98 

99194.67 

28.94 

94.55 

29.36 

94.42 

29.77 

94.29 

30.18 

99 

100 

95.63 

29.24 

.95.50 

29.65 

95.37 

30.07 

95.24 

30.49 

100 

• 

o 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

j Dep. 

Lat. 

6 

o 

c 

at 

<+>» 

■ 

• H 

Q 

73 Deg. 

72} Deg. 

1 

72} 

Deg. 

i 

72} Deg. 

+-> 

to 

c 










































































































S8 


TRAVERSE TABLE. 


Distance.l 

18 Deg. 

18i Deg. 

CO 

r-H 

1 

Deg. 

18| Deg. 

T1 

►— 

r* 

» 

3 

O 

O 

• 

Lat. 

Dep. 

Lat. 

Dep. 

L<it» 

Dep. 

Lat, 

Dep. 

I 

0.95 

0.31 

0.95 

0.31 

0.95 

0.32 

0.95 

0.32 

i 

2 

1.90 

0.62 

1.90 

0.63 

1.90 

0.63 

1.89 

0.64 

2 

3 

2.85 

0.93 

2.85 

0.94 

2 84 

0.95 

2.84 

0.96 

3 

4 

3.80 

1.24 

3.80 

1.25 

3 79 

1.27 

3.79 

1 29 

4 

5 

4.76 

1.55 

4.75 

1.57 

4.74 

1.59 

4.73 

1.61 

5 

6 

5.71 

1.85 

5.70 

1.88 

5.69 

1.90 

5.68 

1.93 

6 

7 

6.66 

2.16 

6.65 

2.19 

6.64 

2.22 

6.63 

2.25 

7 

8 

7.61 

2.47 

7.60 

2.51 

7.59 

2.54 

7.58 

2.57 

8 

9 

8.56 

2.78 

8.55 

2.82 

8.53 

2.86 

8.52 

2.89 

9 

10 

9.51 

3.09 

9.50 

3.13 

9.48 

3.17 

9.47 

3.21 

10 

11 

10.46 

3.40 

10.45 

3.44 

I0.43i 3.49 

10.42 

3.54 

11 

12 

11.41 

3.71 

11.40 

3.76 

11.38 

J. 81 

11.36 

3.86 

12 

13 

12.36 

4 02 

12.35 

4.07 

12.33 

4 12 

12.31 

4.18 

13 

14 

13.31 

4 33 

13.30 

4.38 

13.28 

4.44 

13.26 

4.50 

14 

15 

14.27 

4.64 

14.25 

4.70 

14.22 

4.76 

14.20 

4.82 

15 

16 

15.22 

4.94 

15.20 

5.01 

15.17 

5.08 

15.15 

5.14 

16 

17 

16.17 

5.25 

16.14 

5.32 

16.12 

5.39 

16.10 

5.46 

17 

18 

17.12 

5.56 

17.09 

5.64 

17.07 

5.71 

17.04 

5.79 

18 

19 

18.07 

5.87 

18.04 

5.95 

18.02 

6.03 

17.99 

6.11 

19 

20 

19.02 

6.18 

I* 3 .99 

6.26 

18.97 

6.35 

18.94 

6.-13 

20 

21 

19.97 

6.49 

19.94 

6.58 

19.91 

6.66 

19.89 

6.75 

21 

22 

20.92 

6.80 

20.89 

6.89 

20.86 

6.98 

241.83 

7.07 

22 

23 

21.87 

7.11 

21.84 

7.20 

21.81 

7.30 

21.7S | 

7.39 

23 

24 

22.83 

7.42 

22.79 

7.52 

22.76 

7.62 

22.73 

7 71 

24 

25 

23.78 

7.73 

23.74 

7.83 

23.71 

7.93 

23.67 

8.04 

25 

26 

24.73 

8.03 

24.69 

8.14 

24.66 

8.25 

24.62 

8.36 

26 

27 

25.68 

8.34 

25.64 

8.46 

25.60 

8.57 

25.57 

8.68 

27 

28 

26.63 

8.65 

26.59 

8.77 

26.55 

8.88 

26.51 

9.00 

28 

29 

27.58 

8.96 

27.54 

9.08 

27.50 

9.20 

27.46 

9.32 

28 

30 

28.53 

9.27 

28.49 

9.39 

28.45 

9.52 

28.41 

9.64 

30 

31 

29.48 

9.58 

29.44 

9.71 

29.40 

9.S4 

29.35 

9.96 

31 

32 

30.43 

9.89 

30.39 

10.02 

30.35 

10.15 

30.30 

10.29 

32 

33 

31.38 

10.20 

31.34 

10.33 

31.29 

10.47 

31.25 

10.61 

33 

34 

32.34 

10.51 

32.29 

10.65 

32.24 

10.79 

32.20 

10.93 

34 

35 

33.29 

10.82 

33.24 

10.96 

33.19 

11.11 

33.14 

11.25 

35 

36 

34.24 

11.12 

34.19 

11.27 

34.14 

11.42 

34.09 

11.57 

36 

37 

35.19 

11.43 

35.14 

11.59 

35.09 

11.74 

35.04 

11.89 

37 

38 

36.14 

11.74 

36.09 

11.90 

36.04 

12.06 

35.98 

12.21 

38 

39 

37.09 

12.05 

37.04 

12.21 

36.98 

12.37 

36.93 

12.54 

39 

40 

38.04 

12.36 

37.99 

12.53 

37.93 

12.69 

37.88 

12.86 

40 

41 

38.99 

12.67 

3S.94 

12.84 

38.88 

13.01 

38.82 

13.18 

4i 

42 

39.94 

12.98 

39.89 

13.15 

39.83 

13.33 

39.77 

13.50 

42 

43 

40.90 

13.29 

40.84 

13.47 

40.78 

13.64 

40.72 

13.82 

43 

44 

41.85 

13.60 

41.79 

13.78 

41.73 

13.96 

41 .66 

14.14 

44 

45 

42.80 

13.91 

42.74 

14.09 

42.67 

14.28 

42.61 

14.46 

45 

46 

43.75 

14.21 

43.69 

14.41 

43.62 

14.60 

43.56 

14.79 

46 

47 

44.70 

14.52 

44.64 

14.72 

44.57 

14.91 

44.51 

15.11 

47 

48 

45.65 

14.83 

45.59 

15.03 

45.52 

15.23 

45.45 

15.43 

48 

49 

46.60 

15.14 

46.54 

15.35 

46.47 

15.55 

46.40 

15.75 

49 

50 47.55 

15.45 

47.48 

15.66 

47.42 

15.87 

47.35 

16.07 

50 

CL) 

O 

G 

Dep. 

Lat. 

Dep. 

Lat. 

Lep. 

Lat. 

Dep. 

Lat. 

• 

<u 

o 

c 

G 

l 

00 

' * 

— 

72 Deg. 

711 Deg. 

711 
' 1 2 

Deg. 

7U Deg. 

4-> 

75 
• «■* 

Q 









































































































THAVEHSIS TABLE. 


39 


a 

• 

a 

r-*> 

P3 

18 Deg, 

13$ Deg. 

18^ Deg. 

18| Deg. 

o 

ST 

f* 

& 

3 

n 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

a 

? 

51 

18.50 

15.76 

48.43 

15.97 

48.36 

16.18 

48.29 

16.39 

51 

52 

49.45 

16.07 

49.38 

16.28 

49.31 

16.50 

49.24 

1C 71 

52 

53 

50.41 

16.38 

50.33 

16.60 

50.26 

16.82 

50.19 

17.04 

53 

54 

51.36 

16.69 

51.28 

16.91 

51.21 

17.13 

51.13 

17.36 

54 

55 

52.31 

17.00 

52.23 

17.22 

52.16 

17.45 

52.08 

17.68 

! 55 

66 

53.26 

17.30 

53.18 

17.54 

53.11 

17.77 

53.03 

18.00 

| 56 

57 

54.21 

17.61 

54.13 

17.85 

54.05 

18.09 

53.98 

18.32 

57 

58 

55.16 

17.92 

55.08 

18.16 

55.00 

18.40 

54.92 

18.64 

! 58 

59 

56.11 

18.23 

53.03 

18.48 

55.95 

18.72 

55.87 

18.96 

59 

60 

57.06 

18.54 

56.98 

18.79 

|56.90 

19.04 

56.82 

19.29 

60 

61 

58.01 

18 85 

57.93 

19.10 

57.85 

19.36 

57.76 

19.61 

61 

62 

58.97 

19.16 

58.88 

19.42 

58.80 

19.67 

58.71 

19.93 

62 

63 

59.92 

19.47 

59.83 

19.73 

59.74 

19.99 

i 59.66 

20.25 

63 

64 

60.87 

19.78 

60.78 

20.04 

60.69 

20.31 

| 60.60 

20.57 

64 

65 

61.82 

20.09 

61.73 

20.36 

61.64 

20.62 

61.55 

20.89 

65 

66 

62.77 

20.40 

62.68 

20.67 

62.59 

20.94 

62.50 

21.22 

66 

67 

63.72 

20.70 

63.63 

20.98 

63.54 

21.26 

63.44 

21.54 

67 

68 

64.67 

21.01 

64.58 

21.30 

64.49 

21.58 

64.39 

21.86 

68 

69 

65.62 

21.32 

65.53 

21.61 

65.43 

21.89 

65.34 

22.18 

69 

70 

66.57 

21.63 

66.48 

21.92 

66.38 

22.21 

66.29 

22.50 

70 

71 

67.53 

21.94 

67.43 

22.23 

67.33 

22.53 

67.23 

22.82 

71 

72 

68.48 

22.25 

68.38 

22.55 

68.28 

22.85 

68.18 

23.14 

72 

73 

69.43 

22.56 

69.33 

22.86 

69.23 

23.16 

69.13 

23.47 

73 

74 

70.38 

22.87 

70.28 

23.17 

70.18 

23.48 

70.07 

23.79 

74 

75 

71.33 

23.18 

71.23 

23.49 

71.12 

23.80 

71.02 

24.11 

75 

76 

72.28 

23.49 

72.18 

23.80 

72.07 

24. 12 

71.97 

24.43 

76 

77 

73 23 

23.79 

73.13 

24.11 

73.02 

24.43 

72.91 

24.75 

77 

78 

74.18 

24.10 

74.08 

24.43 

73.97 

24.75 

73.86 

25.07 

78 

79 

75.13 

24.41 

75.03 

24.74 

74.92 

25.07 

74.81 

25.39 

79 

80 

76.08 

24.72 

75.98 

25.05 

75.87 

25.38 

75.75 

25.72 

80 

81 

77.04 

25.03 

76.93 

25.37 

76.81 

25.70 

76.70 

26.04 

81 

82 

77.99 

25.34 

77.88 

25.68 

77.76 

26.02 

77.65 

26.36 

82 

83 

78.94 

25.65 

78.83 

25.99 

78.71 

26.34 

78.60 

26.68 

83 

84 

79.89 

25.96 

79.77 

26.31 

79.66 

26.65 

79.54 

27.00 

84 

85 

80.84 

26.27 

80.72 

26.62 

80.61 

26.97 

80.49 

27.32 

85 

86 

81.79 

26.58 

81.67 

26.93 

81.56 

27.29 

81.44 

27.64 

86 

87 

82.74 

26.88 

82.62 

27.25 

82.50 

27.61 

82.38 

27.97 

87 

88 

83.69 

27.19 

83.57 

27.56 

83.45 

27.92 i 

83.33 

28.29 

88 

89 

84.64 

27.50 

84.52 

27.87 

84.40 

28.24 

84.28 

28.61 

89 

90 

85.60 

27.81 

85.47 

28.18 

85.35 

28.56 

85.22 

28.93 

90 

'91 

86.55 

28.12 

86.42 

28.50 

86.30 

28.37 

86.17 

29.25 

91 

92 

87.50 

28.43 

87.37 

28.81 

87.25 

29.19 

87.12 

29.57 

92 

93 

88.45 

28.74 

88.32 

29.12 

88.19 

29.51 

88.06 

29.89 

93 

94 

89.40 

29.05 

89.27 

29.44 

89.14 

29.83 

89.01 

30.22 

94 

95 

90.35 

29.36 

90.22 

29.75 

90.09 

30.14 

89.96 

30.54 

95 

96 

91.30 

29.67 

91.17 

30.06 

91.04 

30.46 

90.91 

30.86 

96 

97 

92.25 

29.97 

92.12 

30.38 

91.99 

30.78 

91.85 

31.18 

97 

98 

93.20 

30.28 

93.07 

30.69 

92.94 

31.10 

92.80 

31.50 

98 

99 ! 

94.15 

30.59 

94.02 

31.00 

93.88 

31.41 

93.75 

31.82 

99 

100 

95.11 

30.90 

94.97 

31.32 

94.83 

31.73 

94.69 

32 14 

.00 

© 

© 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

©" 

© 

a 

c d 
*-> 

an 

Q 

72 Deg. 

71? De». 

711 Deg. 

71$ Deg. 

Q 














































































































40 


TRAVERSE TABLE. 


o 

• 

V 

r+- 

po 

19 Deg. 

19? Deg. 

ISA 

Deg. 

19? Deg. 

O 

• 

CO 

p 

s 

o 

<9 

* 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lot. 

Dep. 

S3 

o 

® 

1 

0.95 

0.33 

0.94 

0.33 

0.94 

0.33 

0.94 

0,34 

1 

2 

1.89 

0.65 

1.89 

0.66 

1.89 

0.67 

1.88 

0.68 

2 

O 

c 

2.84 

0.98 

2.83 

0.99 

2.83 

1.00 

2 82 

1.01 

3 

4 

3.78 

1.30 

3.78 

1.32 

3.77 

1.34 

3.76 

l 35 

4 

5 

4.73 

1.63 

4.72 

1.65 

4.71 

1.67 

4.71 

1.69 

e 

6 

5.67 

1.95 

5.66 

1.98 

5.66 

2.00 

5.65 

2.03 

6 

7 

6.62 

2.28 

6.61 

? 2.31 

6.60 

2.34 

6.59 

2.37 

7 

8 

7.56 

2.60 

7.55 

2.64 

7.54 

2.67 

7.53 

2.70 

8 

9 

8.51 

2.93 

8.50 

2.97 

8.48 

3.00 

8.47 

3.04 

9 

10 

9.46 

3.26 

9.44 

3.30 

9.43 

3.34 

9.41 

3.38 

10 

11 

10.40 

3.58 

10.38 

3.63 

10.37 

3.67 

10.35 

3.72 

11 

12 

11 .35 

3.91 

11.33 

3.96 

11.31 

4.01 

11.29 

4.06 

12 

13 

12.29 

4.23 

12.27 

4.29 

12.25 

4.34 

12.24 

4.39 

13 

14 

13.24 

4.56 

13.22 

4.62 

13.20 

4.67 

13 18 

4.73 

14 

15 

14.18 

4.88 

14.16 

4.95 

14.14 

5.01 

14.12 

5.07 

15 

16 

15.13 

5.21 

15.11 

5.28 

15.08 

5.34 

15.0® 

5.41 

16 

17 

16.07 

5.53 

16.05 

5.60 

16.02 

5.67 

16 00 

5.74 

17 

18 

17.02 

5.86 

16.99 

5.93 

16.97 

6.01 

16.94 

6.08 

18 

19 

17.96 

6.19 

17.94 

6.26 

17.91 

6.34 

17.88 

6.42 

19 

20 

18.91 

6.51 

18.88 

6.59 

18.85 

6.68 

18.82 

6.76 

20 

21 

19.86 

6.84 

19.83 

6.92 

19.80 

7.01 

19.76 

7.10 

21 

22 

20.80 

7.16 

20.77 

7.25 

20.74 

7.34 

20.71 

7.43 

22 

23 

21.75 

7.49 

21.71 

7.58 

21.68 

7.68 

21.65 / 

7.77 

23 

24 

22.69 

7.81 

22.66 

7.91 

22.62 

8.01 

22.59 

8.11 

24 

25 

23.64 

8.14 

23.60 

8.24 

23.57 

8.35 

23.53( 

8.45 

25 

26 

24.58 

8.46 

24.55 

8.57 

24.51 

8.68 

24.47 

8.79 

26 

27 

25.53 

8.79 

25.49 

8.90 

25.45 

9.01 

25.41 

9.12 

27 

28 

26.47 

9.12 

26.43 

9.23 

26.39 

9.35 

26.35 

9.46 

28 

29 

27.42 

9.44 

27.38 

9.56 

27.34 

9.68 

27.29 

9.80 

29 

30 

28.37 

9.77 

28.32 

9.89 

28.28 

10.01 

28.24 

10.14 

30 

31 

29.31 

10.09 

29.27 

10.22 

29.22 

10.35 

29.18 

10 48 

3i 

32 

30.26 

10.42 

30.21 

10.55 

30.16 

10.68 

30.12 

10 81 

32 

33 

31.20 

10.74 

31.15 

10.88 

31.11 

11.02 

31.06 

1115 

33 

34 

32.15 

11.07 

32.10 

11.21 

32.05 

11.35 

32.00 

11 49 

34 

35 

33.09 

11.39 

33.04 

11.54 

32.99 

11.68 

32.94 

11.83 

35 

36 

34.04 

11.72 

33.99 

11.87 

33.94 

12.02 

33.88 

12.17 

36 

37 

34.98 

12.05 

34.93 

12.20 

34.88 

12.35 

34.82 

12.50 

37 

38 

35.93 

12.37 

35.88 

12.53 

35.82 

12.68 

35.76 

12.84 

38 

39 

36.88 

12.70 

36.82 

12.86 

36.76 

13.02 

36.71 

13.18 

39 

40 

37.82 

13.02 

37.76 

13.19 

37.71 

13.35 

37.65 

13.52 

40 

41 

38.77 

13.35 

38.71 

13.52 

38.65 

13.69 

38.59 

13.85 

41 

42 

39.71 

13.67 

39.65 

13.85 

39.59 

14.02 

1 39.53 

14.19 

42 

43 

40.66 

14.00 

40.60 

14.18 

40.53 

14.35 

40.47 

14.53 

43 

44 

41.60 

14.32 

41.54 

14.51 

41.48 

14.69 

41.41 

14.87 

44 

45 

42.55 

14.65 

42.48 

14.84 

42.42 

15.03 

42.35 

15.21 

45 

16 

43.49 

14.98 

43.43 

15.17 

43.36 

15.36 

43.29 

15.54 

46 

47 

44.14 

15.30 

44.37 

15.50 

44.30 

15.69 

44.24 

15.88 

47 

48 

45.38 

15.63 

45.32 

15.83 

45.25 

16.02 

45.18 

16.22 

48 

49 

46.33 

15.95 

46.26 

16.15 

46.19 

16.36 

46.12 

16.56 

49 

50 

47.28 

16.28 

47.20 

16.48 

47.13 

16.69 

47.06 

16.90 

50 

© 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lklt. 

Dep. 

Lat. 

V 

© 

c 

e$ 

00 

5 

71 Deg. 

70? Deg. 

70j Deg. 

70? Deg. 

d 

*-» 

5 


























































































ao 

P* 

3 

O 

a 

5T 

52 

53 

64 

65 

66 

67 

58 

59 

CO 

61 

62 

63 

64 

65 

66 

67 

68 

69 

JO 

71 

72 

73 

74 

75 

76 

77 

78 

79 

80 

81 

82 

83 

84 

85 

86 

87 

88 

89 

90 

91 

92 

93 

94 

95 

96 

97 

98 

99 

OC 

• 


TRAVERSE TABLE. 


ai 


6.04 

6.99 

7.93 

8.88 

9.82 

0.77 

1.72 

2.66 

3.61 

4.55 


)eg. 

Deg. 


Dog. 

19| Deg. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

16.60 

48.15 

16.81 

48.07 

17.02 

49.00 

17.23 

16.93 

49.09 

17.14 

49.02 

17.30 

48.94 

17.57 

17.26 

50.04 

17.47 

49.96 

17.69 

49.88 

17.91 

17.58 

50.98 

17.80 

50.90 

18.03 

50.82 

19.25 

17.91 

51.92 

18.13 

51.85 

18.36 

51.76 

18.59 

18.23 

52.87 

18.46 

52.79 

18.69 

52.71 

18.92 

18.56 | 

53.81 

18.79 

53.73 

19.03 

53.65 

19.26 

18.88 

54.76 

19.12 

54.67 

19.36 

54.59 

19.60 

19.21 

55.70 

19.45 

55.62 

19.69 

55.53 

19.94 

19.53 

56.65 

19.78 

58.50 

20.03 

56.47 

20.27 

19.86 

57.59 

20.11 

57.50 

20.36 

57.41 

20.61 

20.19 

58.53 

20.44 

58.44 

20.70 

58.35 

20,95 

20.51 

59.48 

20.77 

59.39 

21.03 

59.29 

21.29 

20.84 

60.42 

21.10 

60.33 

21.36 

60.24 

21.63 

21.16 

61.37 

21.43 

01.27 

21.70 

61.18 

21.96 

21.49 

62.31 

21.76 

62.21 

22.03 

62.12 

22.30 

21.81 

63.25 

22.09 

63.10 

22.37 

63.06 

22.64 

22.14 

64.20 

22.42 

64.10 

22.70 

64.00 

22.98 

22.40 

65.14 

22.75 

05.04 

23.03 

64.94 

23.32 

22.79 

66.09 

23.08 

65.98 

23.37 

65.88 

23.65 

23.12 

67.03 

23.41 

66.93 

23.70 

68.82 

23.99 

23.44 

67.97 

23.74 

67.87 

24.03 

67.76 

24.33 

23.77 

68.92 

24.07 

68.81 

24.37 

68.71 

24.67 

24.09 

69.86 

24.40 

69.76 

24.70 

69.65 

25.01 

24.42 

70.81 

24.73 

70.70 

25.04 

70.59 

25.34 

24.74 

71.75 

25.06 

71.64 

25.37 

71.53 

25.68 

25.07 

72.69 

25.39 

72.58 

25.70 

72.47 

26.02 

25.39 

73.64 

25.72 

73.53 

26.04 

73.41 

26.36 

25.72 

74.58 

26.05 

74.47 

26.37 

74.35 

26.70 

26.05 

75.53 

26.38 

75.41 

26.70 

75.29 

27.03 

26.37 

76.47 

26.70 

76.35 

27.04 

76.24 

27.37 

26.70 

77.42 

27.03 

77.30 

27.37 

77.18 

27.71 

27.02 

78.36 

27.36 

78.24 

27.71 

78.12 

28.05 

27.35 

79.30 

27.69 

79.18 

28.04 

79.06 

28.39 

27.67 

80.25 

28.02 

80.12 

28.37 

80.00 

28.72 

28.00 

81.19 

28.35 

81.07 

28.71 

80.94 

29.06 

28.32 

82.14 

28.68 

82.01 

29.04 

81.88 

29.40 

28.65 

83.08 

29.01 

92.95 

29.37 

82.82 

29.74 

28.98 

84.02 

29.34 

83.90 

29.71 

83.76 

30.07 

29.30 

84.97 

29.67 

84.84 

30.04 

84.71 

30.41 

29.63 

85.91 

30.00 

85.78 

30.38 

85.65 

30.75 

29.95 

86.86 

30.33 

86.72 

30.71 

86.59 

31.09 

30.28 

87.80 

30.66 

87.07 

31.04 

87.53 

31.43 

30.60 

88.74 

30.99 

88.61 

31.38 

88.47 

31.76 

30.93 

89.69 

31.32 

89.55 

31.71 

89.41 

32.10 

31.25 

90.63 

31.65 

90.49 

32.05 

90.35 

32.44 

31.58 

91.58 

31.98 

91.44 

32.38 

91.29 

32.78 

31.91 

92.52 

32.31 

92.38 

32.71 

92.24 

33.12 

32.23 

93.46 

32.64 

93.32 

33.05 

93.18 

33.45 

32.56 

94.41 

32.97 

94.26 

33.38 

94.12 

33.79 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

>eg. 

701 Deg. 

70£ 

Deg. 

70J Deg. 


a 

»— • 

p 

3 

O 

CD 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


61 

62 

63 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

80 


81 

82 

83 

84 

85 

86 

87 

88 

89 

90 


91 

92 

93 

94 

95 

96 

97 

98 

99 
100 

• 

ID 

O 

a 

c* * 

«-> 

W 
■—* 

Q 































































































42 


TRAVERSE TABLE 


p 

o 

»—• 
CO 

p 

20 Deg. 

r—- 

20} Deg. 

20 ^ 

Deg. 

20£ Deg. 

C 

w* 

P 

5 

o 

CO 

• 

Lut. 

Dep. 

1-jcLt* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

s 

O 

c 

• 

1 

0.94 

0.34 

0.94 

0.35 

0.94 

0.35 

0.94 

0.35 

1 

1 

2 

1.88 

0.68 

1.88 

0.69 

1.87 

0.70 

1.87 

0.71 

2 

3 

2.82 

1.03 

2.81 

1.04 

2.81 

1.05 

2.81 

1.06 

3 

4 

3.76 

1.37 

3.75 

1.38 

3.75 

i. 40 

3.74 

1.42 

4 

5 

4.70 

1.71 

4.69 

1.73 

4.68 

1.75 

4.68 

1.77 

5 

G 

5.64 

2.05 

5.63 

2.08 

5.62 

2.10 

5.61 

2.13 

6 

7 

6.58 

2.39 

6.57 

2.42 

6.56 

2.45 

6.55 

2.48 

rv 

/ 

8 

7.52 

2.74 

7.51 

2.77 

7.49 

2.80 

7.48 

2.83 

8 

9 

8.46 

3.08 

8.44 

3.12 

8.43 

3.15 

8.42 

3.19 

9 

10 

9.40 

3.42 

9.38 

3.46 

9.37 

3.50 

9.35 

3.54 

i0 

11 

10.34 

3.76 

10.32 

3.81 

10.30 

3.85 

10.29 

3.90 

11 

12 

11.28 

4.10 

11.26 

4.15 

11.24 

4.20 

11.22 

4.25 

12 

13 

12.22 

4.45 

12.20 

4.50 

12.18 

4.55 

12.16 

4.61 

13 

14 

13.16 

4.79 

13.13 

4.85 

13.11 

4.90 

13.09 

4.96 

14 

15 

14.10 

5.13 

14.07 

5.19 

14.05 

5.25 

14.03 

5.31 

15 

16 

15.04 

5.47 

15.01 

5.54 

14.99 

5.60 

14.96 

5.67 

16 

17 

15.97 

5.81 

15.95 

5.88 

15.92 

5.95 

15.90 

6.02 

17 

18 

16.91 

6.16 

16.89 

6.23 

16.86 

6.30 

16.83 

6.38 

18 

19 

17.85 

6.50 

17.83 

6.58 

17.80 

6.65 

17.77 

6.73 

19 

20 

18.79 

6.84 

18.76 

6.92 

18.73 

7.00 

18.70 

7.09 

20 

21 

19.73 

7.18 

19.70 

7.27 

19.67 

7.35 

19.64 

7.44 

21 

22 

20.67 

7.52 

20.64 

7.61 

20.61 

7.70 

20.57 

7.79 

22 

23 

21.01 

•7.87 

21.58 

7.96 

21.54 

8.05 

21.51 

8.15 

23 

24 

22.55 

8.21 

22.52 

8.31 

22.48 

8.40 

22.44 

8.50 

24 

25 

23.49 

8.55 

23.45 

8.65 

23.42 

8.76 

23.38 

8.86 

25 

26 

24.43 

8.89 

24.39 

9.00 

24.35 

9.11 

24.31 

9.21 

26 

27 

25.37 

9.23 

25.33 

9.35 

25.29 

9.46 

25.25 

9.57 

27 

28 

26.31 

9.58 

26.27 

9.69 

26.23 

9.81 

26.18 

9.92 

28 

29 

27.25 

9.92 

27.21 

10.04 

27.16 

10.16 

27.12 

10.27 

29 

30 

28.19 

10.26 

28.15 

10.38 

28.10 

10.51 

28.05 

10.63 

30 

31 

29.13 

10.60 

29.08 

10.73 

29.04 

10.86 

28.99 

10.98 

31 

32 

30.07 

10.94 

30.02 

11.08 

29.97 

11.21 

29.92 

11.34 

32 

33 

31.01 

11.29 

30.96 

11.42 

30.91 

11.56 

30.88 

11.69 

33 

34 

31.95 

11.63 

31.90 

11.77 

31.85 

11.91 

31.79 

12.05 

34 

35 

32.89 

11.97 

32.84 

12.11 

32.78 

12.26 

32.73 

12.40 

35 

36 

33.83 

12.31 

33.77 

12.46 

33.72 

12.61 

33.66 

12.75 

36 

37 

34.77 

12.65 

34.71 

12.81 

34.66 

12.96 

34.60 

13.11 

37 

38 

35.71 

13.00 

35.65 

13.15 

35.59 

13.31 

35.54 

13.46 

38 

39 

36.65 

13.34 

36.59 

13.50 

36.53 

13.66 

36.47 

13.82 

39 

40 

37.59 

13.68 

37.53 

13.84 

37.47 

14.01 

37.41 

14.17 

40 

41 

38.53 

14.02 

38.47 

14.19 

38.40 

14.36 

38.34 

14.53 

~4l 

42 

39.47 

14.36 

39.40 

14.54 

39.34 

14.71 

39.28 

14.88 

42 

43 

40.41 

14.71 

40.34 

14.88 

40.28 

15.06 

40.21 

15.23 

43 

44 

41.35 

15.05 

41.28 

15.23 

41.21 

15.41 

41.15 

15.59 

44 

45 

42.29 

15.39 

42.22 

15.58 

42.15 

15.76 

42.08 

15.94 

45 

46 

43.23 

15.73 

43.16 

15.92 

43.09 

16.11 

43.02 

16.30 

46 

47 

44.17 

16.07 

44.09 

16.27 

44.02 

16.46 

43.95 

16.65 

47 

48 

45.11 

16.42 

45.03 

16.61 

44.96 

16.81 

44.89 

17.01 

48 

49 

46.04 

16.76 

45.97 

16.96 

45.90 

17.16 

45.82 

17.36 

49 

60 

46.98 

17.10 

46.91 

17.31 

46.83 

17.51 

46.76 

17.71 

50 

6 

l 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lr.t. 

d 

o 

c 

I i 

s 

70 Deg. 

69f Deg. 

694 Deg. 

69} Deg. 

■4-» 

VJ 

o 









































































































43 


TBAVEHSE TABLE. 


5 

tt 

P 

20 Deg. 

i 

20* Deg. 

20i 

Deg. 

20| Deg. 

»«• 

CO 

3 

o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lit. 1 

Dep. 

Lat. 

Dep. | 

d 

51 

47.92 

17.44 

47.35 

17.65 

47.77 

17.86 

47.69 

18.07 

5l 

52 

48.86 

17.79 

48.79 

18.00 

48.71 

18.21 

43.63 

18.42 

52 

53 

49.80 

18.13 

49.72 

16.34 

49.64 

18.56 

49.56 

18.78 

53 

54 

50.74 

18.47 

50.66 

18.69 

50.58 

18.91 

50.50 

19.13 

54 

55 

51.68 

18.81 

51.60 

19.04 

51.52 

19.26 

51.43 

19.49 

55 

56 

52.62 

19.15 

52.54 

19.38 

52.45 

19.61 

52.37 

19.84 

56 

57 

53.56 

19.50 

53.48 

19.73 

53.39 

19.96 

53.30 

20.19 

57 

58 

54.50 

19.84 

54.42 

20.07 

54.33 

20.31 

54.24 

20.55 

58 

59 

55.44 

20.18 

55.35 

20.42 

55.26 

20.66 

55.17 

20.90 

59 

60 

56.38 

20.52 

56.29 

20.77 

56.20 

21.01 

56.11 

21.26 

60 

61 

57.32 

20.86 

57.23 

21.11 

57.14 

21.36 

57.04 

21.61 

61 

62 

58.26 

21.21 

58.17 

21.46 

58.07 

21.71 

57.98 

21 .97 

62 

63 

59.20 

21.55 

59.11 

21.8 1 

59.01 

22.06 

58.91 

22.32 

63 

64 

60.14 

21.89 

60.04 

22.15 

59.95 

22.41 

59.85 

22.67 

64 

65 

61.08 

22.23 

60.98 

22.50 

60.88 

22.76 

60.78 

23.03 

65 

66 

62.02 

22.57 

61.92 

22.84 

61.82 

23.11 

61.72 

23.38 

66 

67 

62.96 

22.92 

62.86 

23.19 

62.76 

23.46 

62.65 

23.74 

67 

68 

63.90 

23.26 

63.80 

23.54 

63.69 

23.81 

63.59 

24.09 

68 

69 

64.84 

23.60 

64.74 

23.88 

64.63 

24.16 

64.52 

24.45 

69 

70 

65.78 

23.94 

65.67 

24.23 

65.57 

24.51 

65.46 

24.80 

70 

71 

66.72 

24.28 

66.61 

24.57 

66.50 

24.86 

66.39 

25.15 

71 

72 

67.66 

24.63 

67.55 

24.92 

67.44 

25.21 

67.33 

25.51 

72 

73 

68.60 

24.97 

68.49 

25.27 

68.38 

25.57 

68.26 

25.86 

73 

74 

69.54 

25.31 

69.43 

25.61 

69.31 

25.92 

69.20 

26.22 

74 

75 

70.48 

25.65 

70.36 

25.96 

70.25 

26.27 

70.14 

26.57 

75 

76 

71.42 

25.99 

71.30 

26.30 

71.19 

26.62 

71.07 

26.93 

76 

77 

72.36 

26.34 

72.24 

26.65 

72.12 

26.97 

72.01 

27.28 

77 

78 

73.30 

26.68 

73.18 

27.00 

73.06 

27.32 

72.94 

27.63 

78 

79 

74.24 

27.02 

74.12 

27.34 

74.00 

27.67 

73.88 

27.99 

79 

80 

75.18 

27.36 

75.06 

27.69 | 

74.93 

28.02 

74.81 

28.34 

80 

81 

76.12 

27.70 

75.99 

28.04 

75.87 

28.37 

75.75 

28.70 

81 

82 

77.05 

28.05 

76.93 

28.38 

76.81 

28.72 

76.68 

29.05 

82 

83 

77.99 

28.39 

77.87 

28.73 

77.74 

29.07 

77.62 

29.41 

83 

84 

78.93 

28.73 

78.81 

29.07 

78.68 

29.42 

78.55 

29.76 

84 

85 

79.87 

29.07 

79.75 

29.42 

79.62 

29.77 

79.49 

30.11 

85 

86 

80.81 

29.41 

80.68 

29.77 

80.55 

30.12 

180.42 

30.47 

86 

87 

81.75 

29.76 

81.62 

30.11 

81.49 

30.47 

!81.36 

30.82 

87 

88 

82.69 

30.10 

82.56 

30.46 

82.43 

30.82 

82.29 

31.18 

88 

89 

83.63 

30.44 

83.50 

30.80 

83.36 

31.17 

83.23 

31.53 

89 

90 

84.57 

30.78 

84.44 

31.15 

84.30 

31.52 

84.16 

31.89 

90 

91 

85.51 

31.12 

85.38 

31.50 

85.24 

31.87 

85.10 

32.24 

91 

92 

86.45 

31.47 

86.31 

31.84 

86.17 

32.22 

86.03 

32.59 

92 

93 

87.39 

31.81 

87.25 

32.19 

87.11 

32.57 

86.97 

32.95 

93 

94 

88.33 

32.15 

88.19 

32.54 

88.05 

32.92 

87.90 

33.30 

94 

95 

89.27 

32.49 

89.13 

32.88 

88 .9S 

33.27 

88.84 

33.66 

95 

96 

90.21 

32.83 

90.07 

33.23 

89.92 

33.62 

89.77 

34.01 

96 

97 

91.15 

33.18 

91.00 

33.57 

90.86 

33.97 

90.71 

34,37 

97 

98 

92.09 

33.52 

91.94 

33.92 

91.79 

34.32 

91.64 

34.72 

98 

99 

93.03 

33.86 

92.88 

34.27 

92.73 

34.67 

92.58 

35.07 

99 

100 

93.97 

34.20 

93.82 

34.61 

93.67 

35.02 

93.51 

35.43 

100 

6 

O 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

8 

c 

a) 

CO 

• 

c 

70 Deg. 

69| Deg. 

69| 

Deg. 

69$ Deg 

vd 

LL 

. •—* 










































































































44 


TRAVERSE TABLE 


Distance.l 

21 Dog. 

1 

21$ Deg. 

211 Deg. 

2if Deg. 

f Distance, j 

Lat. 

Dep. 

JLi tit • 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.93 

0.36 

0.93 

0.36 

0.93 

0.37 

0.93 

0.37 

1 

2 

1.87 

0.72 

1.86 

0.72 

1.86 

0.73 

1.86 

0.74 

2 

3 

2.80 

1 . 08 

2.80 

1.09 

2.79 

1.10 

2.79 

1.11 

3 

A 

« 

3.73 

1.43 

3.73 

1.45 

3.72 

1.47 

3.72 

1.48 

4 

h 

4.G7 

1.79 

4.66 

1.81 

4.65 

1.83 

4.64 

1 .85 

5 

6 

5. GO 

2.15 

5.59 

2.17 

5.58 

2.20 

5.57 

2.22 

6 

7 

G. 54 

2.51 

6.52 

2.54 

6.51 

2.57 

6.50 

2.59 

7 

1 8 

7.47 

2.87 

7.46 

2.90 

7.44 

2.93 

7.43 

2.96 

8 

<J 

8.40 

3.23 

8.39 

3.26 

8.37 

3.30 

8.36 

3.34 

9 

10 

9.34 

3.58 

9.32 

3.62 

9.30 

3.67 

9.29 

3.71 

10 

11 

10.27 

3.94 

10.25 

3.99 

10.23 

4.03 

10.22 

4.08 

11 

12 

11.20 

4.30 

11.18 

4.35 

11.17 

4.40 

11.15 

4.45 

12 

13 

12.14 

4.66 

12.12 

4.71 

12.10 

4.76 

12.07 

4.82 

13 

14 

13.07 

5.02 

13.05 

5.07 

13.03 

5.13 

13.00 

5.19 

14 

15 

14.00 

5.38 

13.98 

5.44 

13.96 

5.50 

13.93 

5.56 

15 

1G 

14.94 

5.73 

14.91 

5.80 

14.89 

5.86 

14.86 

5.93 

16 

17 

15.87 

6.09 

15.84 

6.16 

15.82 

6.23 

15.79 

6.30 

17 

18 

16.80 

6.45 

16.78 

6.52 

16.75 

6.60 

16.72 

6.67 

18 

19 

17.74 

6.81 

17.71 

6.89 

17.63 

6.96 

17.65 

7.04 

19 

20 

18.67 

7.17 

18.64 

7.25 

18.61 

7.33 

18.58 

7.41 

20 

21 

19.61 

7.53 

19.57 

7.61 

19.54 

7.70 

19.50 

7.78 

21 

22 

20.54 

7.88 

20.50 

7.97 

20.47 

8.06 

20.43 

8.15 

22 

23 

21.47 

8.24| 

21.44 

8.34 

21.40 

8.43 

21.36 

8.52 

23 

24 

22.41 

8.60 

22.37 

8.70 

22.33 

8.80 

22.29 

8.89 

24 

25 

23.34 

8.96 

23.30 

9.06 

23.26 

9.16 

23.22 

9.26 

25 

2G 

24.27 

9.32 

24.23 

9.42 

24.19 

9.53 

24. 15 

9.63 

26 

27 

25.21 

9.68 

25.16 

9.79 

25.12 

9.90 1 

25.08 

10.01 

27 

28 

2G.14 

10.03 

26.10 

10.15 

26.05 

10.26 

26.01 

10 38 

28 

29 

27.07 

10.39 

27.03 

10.51 

26.98 

10.63 

26.94 

10.75 

29 

30 

28.01 

10.75 

27.96 

10.87 

27.91 

11.00 

27.86 

11.12 

30 

31 

28.94 

11.11 

28.89 

11.24 

23.84 

11.36 

28.79 

11.49 

31 

32 

29.87 

11.47 

29.82 

11.60 

29.77 

11.73 

29.72 

11.86 

32 

33 

30.81 

11.83 

30.76 

11.96 

30.70 

12.09 

30.65 

12.23 

33 

34 

31.74 

12.18 

31.69 

12.32 

31.63 

12.46 

31.58 

12.60 

34 

35 

32.68 

12.54 

32.62 

12.69 

32.56 

12.83 

32.51 

12.97 

35 

3G 

33.61 

12.90 

33.55 

13.05 

33.50 

13.19 

33.44 

13.34 

36 

37 

34.54 

13.26 

34.48 

13.41 

34.43 

13.56 

34.37 

13.71 

37 

38 

35.48 

13.62 

35.42 

13.77 

35.36 

13.93 

35.29 

14.08 

38 

39 

36.41 

13.98 

36.35 

14.14 

36.29 

14.29 

36.22 

14.45 

39 

40 

37.34 

14.33 

37.28 

14.50 

37.22 

14.66 

37.15 

14.82 

40 

41 

38.28 

14.69 

33.21 

14.86 

38.15 

15.03 

38.08 

15.19 

41 

42 

39.21 

15.05 

39. 14 

15.22 

39.08 

15.39 

39.01 

15.56 

42 

43 

40.14 

15.41 

40.08 

15.58 

40.01 

15.76 

39.94 

15.93 

43 

44 

41.08 

15.77 

41.01 

15.95 

40.94 

16.13 

40.87 

16.30 

44 

45 

42.01 

16.13 

41.94 

16.31 

41.87 

16.49 

41.80 

16.68 

45 

46 

42.94 

16.48 

42.87 

16.67 

42.80 

16.86 

42.73 

17.05 

46 

47 

43.88 

16.84 

43.80 

17.03 

43.73 

17.23 

43.65 

17.42 

47 

48 

44.81 

17.20 

44.74 

17.40 

44.66 

17.59 

44.58 

17.79 

48 

49 

45.75 

17.56 

45.67 

17.76 

45.59 

17.96 

45.51 

18.16 

49 

DO 

46.68 

17.92 

46.60 

18.12 

46.52 

18.33 

46.44 

18.53 

50 

« 

9 

O 

c 

Dep. 

Lat. 

Dep. 

Lat. 

\ 

Dep. 

Lat. 

Dep. 

Lat. 

gJ 

o 

c 

cj 

To 
• —< 

i 

69 Deer. 

O 

63$ Deg 

i 631 

Deg. 

63$ Dog. 

«-» 

m 

£1 





































































































TKAVEItSE TABLE 


45 


t; 

K • 

Ol 

p 

21 Deg. 

2li Deg. 

21 j Deg. 

21| 

Deg 

<—> 


C 

K 

P5 

(3 

ID 

CD 

• 

Lat. 

Dep. 

Lat. 

Dep. 

LcLt* 

Dep. 

Lat. 

Dep. 

.3 

a 

o 

51 

47.61 

18.28 

47.53 

18.48 

47.45 

18.69 

47.37 

18. 

90 

5! 

52 

48.55 

18.64 

48.46 

18.85 

48.38 

19.06 

48.30 

19. 

27 

52, 

53 

49.48 

18.99 

49.40 

19,21 

49.31 

19.42 

49.23 

19. 

64 

511 

64 

50.41 

19.35 

50.33 

19.57 

50.24 

19.79 

50.16 

20. 

01 

51 

55 

51 35 

19.71 

51.26 

19.93 

51.17 

20.16 

51.08 

20. 

39 

55 

56 

52 28 

20.07 

52.19 

20.30 

52.10 

20.52 

52.01 

20. 

75 

56 

57 

53 21 

20.43 

53.12 

20.66 

53.03 

20.89 

52.94 

21. 

12 

8< 

58 

54.15 

20.79 

54.06 

21.02 

53.96 

21.26 

53.87 

21. 

49 

58 

59 

55.08 

21.14 

54.99 

21.38 

54.89 

21.62 

54.80 

21. 

86 

59 

60 

56.01 

21.50 

55.92 

21.75 

55.83 

21.99 

55.73 

22. 

23 

60 

61 

56.95 

21.86 

56.85 

22.11 

56.76 

22.36 

56.66 

22. 

60 

61 

62 

57: 83 

22.22 

57.78 

22.47 

57.69 

22.72 

57.59 

22. 

97 

62 

63 

58.82 

22.58 

58.72 

22.83 

58.62 

23.09 

58.52 

23. 

35 

63 

64 

59.75 

22.94 

59.65 

23.20 

59.55 

23.46 

59.44 

23. 

72 

64 

65 

60.68 

23.29 

60.58 

23.56 

60.48 

23.82 

60.37 

24. 

09 

65 

66 

61.62 

23.65 

61.51 

23.92 

61.41 

24.19 

61.30 

24. 

46 

66 

67 

62.55 

24.01 

62.44 

24.28 

62.34 

24.56 

62.23 

24. 

83' 

67 

68 

63.48 

24.37 

63.38 

24.65 

63.27 

24.92 

63.16 

• 

20 

68 

69 

64.42 

24.73 

64.31 

25.01 

64.20 

25.29 

64.09 

25. 

57 

69 

70 

65.35 

25.09 

65.24 

25.37 

65.13 

25.66 

65.02 

25. 

94 

70 

71 

66.28 

25.44 

66.17 

25.73 

66.06 

26.02 

65.95 

26. 

31 

71 

72 

67.22 

25.80 

67.10 

26.10 

66.99 

26.39 

66.87 

26. 

63 

72 

73 

68.15 

26.16 

68.04 

26.46 

67.92 

26.75 

67.80 

27. 

05 

73 

74 

69.08 

26.52 

68.97 

26.82 

68.85 

27.12 

68.73 

27. 

42 

74 

75 

70.02 

26.88 

69.90 

27.18 

69.78 

27.49 

69.66 

27. 

79 

75 

76 

70.95 

27.24 

70.83 

27.55 

70.71 

27.85 

70.59 

28. 

16 

76 

77 

71.89 

27.59 

71.76 

27.91 

71.64 

28.22 

71.52 

28 

53 

77 

78 

72.82 

27.95 

72.70 

28.27 

72.57 

28.59 

72.45 

28 

90 

76 

79 

73.75 

28.31 

73.63 

28.63 

73.50 

28.95 

73.38 

29 

27 

79 

80 

74.69 

28.67 

74.56 

29.00 

74.43 

29.32 

74.30 

29 

64 

80 

81 

75.62 

29.03 

75.49 

29.36 

75.36 

29.69 

75.23 

30 

02 

81 

82 

76.55 

29.39 

76.42 

29,. 72 

76.29 

30.05 

76.16 

30 

39 

82 

83 

77.49 

29.74 

77.30 

30.08 

77.22 

30.42 

77.09 

30 

.76 

83 

84 

78.42 

30.10 

78.29 

30.44 

78.16 

30.79 

78.02 

31 

.13 

84 

85 

79.35 

30.46 

79.22 

30.81 

79.09 

31.15 

78.95 

31 

.50 

85 

86 

80.29 

30.82 

80.15 

31.17 

80.02 

31.52 

79.88 

31 

.87 

80 

87 

81.22 

31.18 

81.08 

31.53 

80.95 

31.89 

80.81 

32 

.24 

87 

88 

82.16 

31 54 

82.02 

31.89 

81.88 

32.25 

81.74 

32 

.61 

88 

89 

83.09 

31.89 

82.95 

32.26 

82.81 

32.62 

82.66 

32 

.98 

89 

90 

84.02 

32.25 

83.88 

32.62 

83.74 

32.99 

83.59 

33 

.35 

90 

91 

84.96 

32.61 

84.81 

32.98 

84.67 

33.35 

84.52 

33 

.72 

91 

92 

85.89 

32.97 

85.74 

33.34 

85.60 

33.72 

85.45 

34 

.09 

92 

93 

86.82 

33.33 

86.68 

33.71 

86.53 

34.08 

86.38 

34 

.46 

93 

94 

87.76 

33.89 

87.61 

34.07 

87.46 

34.45 

87.31 

34 

.83 

91 

95 

88.69 

34.04 

88.54 

34.43 

88.39 

34.82 

88.24 

35 

.20 

95 

96 

89.62 

34.40 

89.47 

34.79 

89.32 

35.18 

89.17 

35 

.57 

96 

97 

90.56 

34.76 

90.40 

35.16 

90.25 

35.55 

90.09 

35 

.94 

97 

98 

91.49 

35.12 

91.34 

35.52 

|91.18 

35.92 

91.02 

36 

.31 

98 

99 

92.42 

35.48 

92.27 

35.88 

92.11 

36.28 

91.95 

36 

.69 

99 

100 

93.36 

35.84 

93.20 

36.24 

93 . 04 

36 . 65 

92.88 

37 

.06 

100 

© 

V 

e 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I 

Dep. 

Lat. 

© 

o 

c 

e i 

CD 

5 

69 Deg. 

68f 

Deg. 

G8j 

Deg. 

68$ 

Dog 

d 

in 

5 


22 












































































































46 


TRAVERSE TABLE. 


\ Distance j 

1 

22 Dog. 

22\ Dog. 

22\ 

Deg. 

22| Deg. 

1 

o 

00 

r* 

m 

3 

a 

a 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.93 

0.37 

0.93 

0.38 

0.92 

0.38 

0.92 

0.39 

1 

2 

1.85 

0.75 

1.85 

0.76 

1.85 

0.77 

1.84 

0.7 7 

2 

3 

2.78 

1.12 

2.73 

1.14 

2.77 

1.15 

2.77 

1.16 

3 

4 

3.71 

1.50 

3.70 

1.51 

3.70 

1.53 

3.69 

* .55 

4 

5 

4.64 

1.87 

4.63 

1.89 

4.62 

1.91 

4.61 

i .93 

5 

6 

5.56 

2.25 

5.55 

2.27 

5.54 

2.30 

5.53 

2.32 

6 

7 

6.49 

2.62 

6.48 

2.65 

6.47 

2.68 

6.46 

2 ..71 

7 

8 

7.42 

3.00 

7.40 

3.03 

7.39 

3.06 

7 38 

3.09 

8 

9 

8.34 

3.37 

8.33 

3.41 

8.31 

3.44 

8.30 

3.48 

9 

10 

9.27 

3.75 

9.26 

3.79 

9.24 

3.83 

Q OO 

J • ** At 

3.87 

10 

11 

10.20 

4.12 

10.18 

4.17 

10.16 

4.21 

10.14 

4.25 

11 

12 

11.13 

4.50 

11.11 

4.54 

11.09 

4.59 

11.07 

4.64 

12 

13 

12.05 

4.87 

12.03 

4.92 

12.01 

4.97 

11.99 

5.03 

13 

14 

12.98 

5.24 

12.96 

5.30 

12.93 

5.36 

12.91 

5.41 

14 

15 

13.91 

5.62 

13.88 

5.68 

13.86 

5.74 

13.83 

5.80 

15 

16 

14.83 

5.99 

14.81 

6.06 

14.78 

6.12 

14.76 

6.19 

16 

17 

15.76 

6.37 

15.73 

6.44 

15.71 

6.51 

15.68 

6.57 

17 

18 

16.69 

6.74 

16.66 

6.82 

16.63 

6.89 

16.60 

6.96 

18 

19 

17.62 

7.12 

17.59 

7.19 

17.55 

7.27 

17.52 

7.35 

19 

20 

18.54 

7.49 

18.51 

7.57 

18.48 

7.65 

18.44 

7.73 

20 

21 

19.47 

7.87 

19.44 

7.95 

19.40 

8.04 

19.37 

8 . 12 

21 

22 

20.40 

8.24 

20.36 

8.33 

20.33 

8.42 

20.29 

8.51 

22 

23 

21.33 

8.62 

21.29 

8.71 

21.25 

8.80 

21.21 

8.89 

23 

24 

22.25 

8.99 

22.21 

9.09 

22.17 

9.18 

22.13 

9.28 

24 

25 

23.18 

9.37 

23.14 

9.47 

23.10 

9.57 

23.05 

9.67 

25 

26 

24.11 

9.74 

24.06 

9.84 

24.02 

9.95 

|23.98 

10.05 

26 

27 

25.03 

10.11 

24.99 

10.22 

24.94 

10.33 

24.90 

10.44 

27 

28 

25.96 

10.49 

25.92 

10.60 

25.87 

10.72 

;25.82 

10.83 

28 

20 

26.89 

10.86 

26.84 

10.98 

26.79 

11.10 

26.74 

11.21 

29 

30 

27.82 

11.24 

27.77 

11.36 

27.72 

11.48 

27.67 

11.60 

30 

' 31 

28.74 

11.61 

28.69 

11.74 

28.64 

11.86 

28.59 

11.99 

31 

32 

29.67 

11.99 

29.62 

12.12 

29.56 

12.25 

29.51 

12.37 

32 

33 

30.60 

12.36 

30.54 

12.50 

30.49 

12.63 

30.43 

12.76 

33 

34 

31.52 

12.74 

31.47 

12.87 

31.41 

13.01 

31.35 

13.15 

34 

35 

32.45 

13.11 

32.39 

13.25 

32.34 

13.39 

32.28 

13.53 

35 

36 

33.33 

13.49 

33.32 

13.63 

33.26 

13.78 

33.20 

13.92 

36 

37 

34.31 

13.86 

34.24 

14.01 

34.18 

14.16 

34.12 

14.31 

37 

38 

35.23 

14.24 

35.17 

14.39 

35.11 

14.54 

35.04 

14.70 

38 

39 

36.16 

14.61 

36.10 

14.77 

36.03 

14.92 

35.97 

15.08 

39 

40 

37.09 

14.98 

37.02 

15.15 

36.96 

15.31 

36.89 

15.47 

40 

41 

33.01 

15.36 

37.95 

15.52 

37.88 

15- 69 

37.81 

15.86 

11 

42 

38.94 

15.73 

38.87 

15.90 

33.80 

16.07 

38.73 

16.24 

42 

43 

39.87 

16.11 

39.80 

16.28 

39.73 

16.46 

39.65 

16.63 

43 

44 

40.80 

16.48 

40.72 

16.66 

40.65 

16.84 

40.58 

17.02 

44 

45 

41.72 

16.86 

41.65 

17.04 

41.57 

17.22 

41.50 

17.40 

45 

46 

42.65 

17.23 

42.57 

17.42 

12.50 

17.60 

42.42 

17.79 

46 

47 

43.58 

17.61 

43.50 

17.80 

43.42 

17.99 

43.34 

18.18 

47 

48 

44.50 

17.98 

44.43 

18.18 

44.35 

18.37 

44.27 

18.56 

48 

49 

45.43 

18.36 

45.35 

18.55, 

45.27 

18.75 

45.19 

18.95 

49 

60 

46.36 

18.73 

46.28 

18.93 

46.19 

19.13 

46.11 

19.34 

50 

© 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

V 

V 

c 

ri 

w 

a 

' 

Q 

68 Dog. 

671 Deg. 

G7i Deg. 

67$ Deg. 

1 

3 

00 

• H 

rj 

i 




































































































TRAVERSE TABLE, 


47 


© 

s* 

22 Deg. 

221 Deg. 

22 £ 

|i 

Deg. j 

1 

221 Deg. 

a 

c/a 

<-*• 

© 

i u ii.'L* | 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 1 

Lat. 

Dep. 

3 

o 

a 

51 

47.29 

19.10 

47.20 

19.31 i 

47.12 

19.52 

17.03 

19.72 

51 

52 

48.21 

19.48 

48.13 

19.69 1 

48.04 

19.90 

47.95 

20.11 ! 

52 

53 

49.14 

19.85 

49.05 

20.07 

48.97 

20.28 

48.88 

20.50 ! 

53 

64 

50.07 

20.23 

49.98 

20.45 

49.89 

20.66 

49.80 

20.88 

54 

55 

51.00 

20.60 

50.90 

20.83 

50.81 

21.05 

50.72 

21.27 

55 

56 

51.92 

20.98 

51.83 

21.20 

51.74 

21.43 

51.64 

21.66 

00 

57 

52.85 

21.35 

52.7 6 

21.58 

52.66 

21.81 

52.57 

22.04 

57 

58 

53.78 

21.73 

53.68 

21.96 

53.59 

22.20 

53.49 

22.43 

58 

59 

54.70 

22.10 

54.61 

22.34 

54.51 

22.58 

54.41 

22.82 

59 

60 

55.63 

22.48 

55.53 

22.72 

55.43 

22.96 

55.33 

23.20 

60 

61 

56.56 

22.85 

56.47 

23.10 

56.36 

23.34 

56.25 

23.59 

61 

62 

57.49 

23.23 

57.38 

23.48 

57.28 

23.73 

57.18 

23.98 

62 

63 

58.41 

23.60 

58.31 

23.85 

58.20 

24.11 

58.10 

24.38 

63 

61 

59.34 

23.97 

59.23 

24.23 

59.13 

24.49 

59.02 

24.75 

64 

65 

60.27 

24.35 

60.16 

24.61 

60.05 

24.87 

59.94 

25.14 

65 

66 

61.19 

24.72 

61.09 

24.99 

60.98 

25.26 

60.87 

25.52 

66 

67 

62.12 

25.10 

62.01 

25.37 

61.90 

25.64 

61.79 

25.91 

67 

68 

63.05 

25.47 

62.94 

25.75 

62.82 

26.02 

62.71 

26.30 

68 

69 

63.98 

25.85 

63.86 

26.13 

63.75 

26.41 

63.63 

26.68 

69 

70 

64.90 

26.22 

64.79 

26.51 

64.67 

26.79 

64.55 

27.07 

70 

71 

65.83 

26.60 

65.7! 

26.88 

65.60 

27.17 

65.48 

27.46 

71 

72 

66.76 

26.97 

66.64 

27.26 

66 52 

27.55 

66.40 

27.84 

72 

73 

67.68 

27.35 

67.56 

27.64 

67.44 

27.94 

67.32 

28.23 

73 

74 

68.61 

27.72 

68.49 

28.02 

68.37 

28.32 

68.24 

28.62 

74 

75 

69.54 

28.10 

69.42 

28.40 

69.29 

28.70 

69.17 

29.00 

75 

j 76 

70.47 

28.47 

70.34 

28.78 

70.21 

29.08 

70.09 

29.39 

76 

; 77 

71.39 

28.84 

71.27 

29.16 

71.14 

29.47 

71.01 

29.78 

77 

78 

72.32 

29.22 

72.19 

29.53 

72.06 

29.85 

71.93 

30.16 

78 

79 

73.25 

29.59 

73.12 

29.91 

72.99 

30.23 

72.85 

30.55 

79 

80 

74.17 

29.97 

74.04 

30.29 

73.91 

30.61 

73.78 

30.94 

j 80 

81 

75.10 

30.34 

74.97 

30.67 

74.83 

31 .00 

74.70 

31.32 

81 

82 

76.03 

30.72 

75.89 

31.05 

75.76 

31.38 

75.62 

31.71 

82 

83 

76.96 

31.09 

76.82 

31.43 

76.68 

31.76 

76.54 

32.10 

83 

81 

77.88 

31.47 

77.75 

31.81 

77.61 

32.15 

77.46 

32.48 

84 

85 

78.81 

31.84 

78.67 

32.19 

78.53 

32.53 

78.39 

32.87 

85 

86 

79.74 

32.22 

79.60 

32.56 

79.45 

32.91 

79.31 

33.26 

86 

87 

80.66 

32.59 

80.52 

32.94 

80.38 

33.29 

80.23 

33.64 

87 

88 

81.59 

32.97 

81.45 

33.32 

81.30 

33.68 

81.15 

34.03 

88 

89 

82.52 

33.34 

82.37 

33.70 

82.23 

34.06 

82.08 

34.42 

89 

90 

83.45 

33.71 

83.30 

34.08 

83.15 

34.44 

83.00 

34.80 

90 

91 

84.37 

34.09 

84.22 

34.46 

84.07 

34.82 

83.92 

35.19 

91 

92 

85.30 

34.46 

85.15 

34.84 

85.00 

35.21 

84.84 

35.58 

92 

1 93 

86.23 

34.84 

86.08 

35.21 

85.92 

35.59 

85.76 

35.90 

93 

94 

87.16 

35.21 

87.00 

35.59 

86.84 

35.97 

86.69 

36.35 

94 

j 95 

88.08 

35.59 

87.93 

35.97 

87.77 

36.35 

87.61 

36.74 

9fi 

\ 96 

89.01 

35.96 

88.85 

36 35 

88.69 

36.74 

88.53 

37.12 

96 

97 

89.94 

36.34 

89.78 

36.73 

89.62 

37.12 

89.45 

37 51 

97 

98 

90.86 

36.71 

90.70 

37.11 

90.54 

37.50 

90.38 

37.90 

98 

99 

91.79 

37.09 

91.63 

37.49 

91.46 

37.89 

91.30 

38.28 

99 

100 

92.72 

37.46 

92.55 

37,86 

92.39 

38.27 

92.22 

38.67 

100 

6 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

i 

Dep. 

Lat. 

Dep. 

Lat. 

1 

© 

o 

I s 

c3 

<*-> 

c/a 

£ 

68 Deg. 

671 Deg. 

G7£ Deg. 

! 671 Deg. 

! 

! .2 

i Q 















































































































48 


TRAVERSE TABfi-E 


o 

cr 

e+ 

23 Deg. 

23} Deg. 

23| Deg. 

23| Deg. 

5 

tn’ 

r-*- 

P ; 

P 

o 

o 

•' 

Lat. 

Dep. 

ILctt. 

Dep. 

Lat. 

L>ep. 

Lat. 

Dep. 

S3 

r. 

« 

i ' 1 

0,92 

0.39 

0.92 

0.39 

0.92 

0.40 

0.92 

0.40 

1 * 

2 

1.84 

0.78 

1.84 

0,79 

1.83 

0.80 

1.83 

0.81 

o 

A» 

I 3 

2.76 

1.17 

2.76 

1.18 

2.75 

1.20 

2.75, 

1.21 

3 i 

4 

8.68 

1.56 

3.68 

1.58 

3.67 

1.59 

3.66 

1.61 

y 

! 5 

A.GO 

1.95 

4.59 

1.97 

4.59 

1.99 

4.58 

2.01 

3 ' 

6 

5.52 

2.34 

5.51 

2.37 

5.50 

2.39 

5.49 

2.42 

6 

7 

6.44 

2.74 

6.43 

2.76 

6.42 

2.79 

6.41 

2.82 

7 1 

8 

7.36 

3.13 

7.35 

3.16 

7.34 

3.19 

7.32- 

3.22 

8 * 

9 

8.28 

3.52 

8.27 

3.55 

8.25 

3.59 

8.24 

3.62 

9 

10 

9.20 

3.91 

9.19 

3.95 

9.17 

3.99 

9.15 

4.03 

*0 

11 

10.13 

4.30 

10.11 

4.34 

10.09 

4.39 

10.07 

4.43 

ii ] 

12 

11.05 

4.69 

11.03 

4.74 

11.00 

4.78 

10.98 

4.83 

12 

13 

11.97 

5.08 

11.94 

5.13 

11.92 

5.18 

11.90 

5.24 

13 \ 

1 - i 

14 

12.89 

5.47 

12.86 

5.53 

12.84 

5.58 

12.81 

5.64 

14 - 

15 

13.81 

5.86 

13.78 

5.92 

13.76 

5.98 

13.73 

6.04 

15 [ 

10 

14.73 

6.25 

14.70 

6.32 

14.67 

6.38 

14.64 

6.44 

i6 s 

17 

15.65 

6.64 

15.62 

6.71 

15.59 

6.78 

15.56 

6.85 

17 1 

18 

16.57 

7.03 

16.54 

7.11 

16.51 

7.18 

16.48 

7.25 

18 s 

19 

17.49 

7.42 

17.46 

7.50 

17.42 

7.58 

17.39 

7.65 

19 : 

20 

18.41 

7.81 

18.38 

7.89 

18.34 

7.97 

18.31 

8.05 

20 | 

21 

19.33 

8.21 

19.29 

8.29 

19.26 

8.37 

19.22 

8.46 

21 [ 

22 

20.25 

8.60 

20.21 

8.68 

20.18 

8.77 

20.14 

8.86 

22 

23 

21.17 

8.99 

21.13 

9.08 

21.09 

9.17 

21.05 

9.26 

23 ' 

24 

22.09 

9.38 

22.05 

9.47 

22.01 

9.57 

21.97 

9.67 

24 ; 

25 

23.01 

9.77 

22.97 

9.87 

22.93 

9.97 

22.88 

10.07 

25 ; 

26 

23.93 

j0.16 

23.89 

10.26 

23.84 

10.37 

23.80 

10.47 

26 

27 

24.85 

,0.55 

24.81 

10.66 

24.76 

10.77 

24.71 

10.87 

27 ! 

28 

25.77 

,0.94 

25.73 

11.05 

25.68 

11.16 

25.63 

11.28 

28 

29 

26.69 

U.33 

26.64 

11.45 

26.59 

11.56 

26.54 

11.68 

29 

30 

27.62 

11.72 

27.56 

11.84 

27.51 

11.96 

27.46 

12.08 

30 

31 

28.54 

12.11 

28.48 

12.24 

28.43 

12.36 

28.37 

12.49 

31 

32 

29.46 

12.50 

29.40 

12.63 

29.35 

12.76 

29.29 

12.89 

32 

33 

30.38 

12.89 

30.32 

13.03 

30.26 

13.16 

30.21 

13.29 

33 

34 

31.30 

13.28 

31.24 

13.42 

31.18 

13.56 

31.12 

13.69 

34 

35 

32.22 

13.68 

32.16 

13.82 

32.10 

13.96 

32.04 

14.10 

35 

36 

33.14 

14.07 

33.08 

14.21 

33.01 

14.35 

32.95 

14.50 

36 

37 

34.06 

14.46 

34.00 

14.61 

33.93 

14.75 

33.87 

14.90 

37 

38 

34.98 

14.85 

34.91 

15.00 

34.85 

15.15 

34.78 

15.30 

38 

39 

35.90 

15.24 

35.83 

15.39 

35.77 

15.55 

35.70 

15.71 

l 39 

40 

36.82 

15.63 

36.75 

15.79 

36.68 

15.95 

36.61 

16.11 

40 

41 

37.74 

16.02 

37.67 

16.18 

37.60 

16.35 

37.53 

16.51 

41 

42 

38.66 

16.41 

38.59 

16.58 

38.52 

16.75 

38.44 

16.92 

! 42 

43 

39.58 

16.80 

39.51 

16.97 

39.43 

17.15 

39.36 

j 17.32 

1 43 

44 

40.50 

17.19 

40.43 

17.37 

40.35 

17.54 

40.27 

17.',2 

41 

45 

41.42 

17.58 

41.35 

17.76 

41.27 

17.94 

141.19 

18.12 

45 

46 

42.34 

17.97 

42.26 

18.16 

42.18 

18.34 

142.10 

18.53 

46 

47 

43.26 

18.36 

43.18 

18.55 

43.10 

18.74 

43.02 

18.93 

47 

48 

44.18 

18.76 

44.10 

18.95 

44.02 

19.14 

43.93 

19.33 

48 

19 

45.10 

19.15 

45.02 

19.34 

44.94 

19.54 

44.85 

19.73 

49 

50 

46.03 

19.54 

45.94 

19.74 

45.85 

19.94 

1 45.77 

20.14 

50 

© 

1 5 

i Dep. 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lett • 

Dep. 

Lcit* 

'© 

o 

c 

a d 

(A 

S 

1 

67 Deg 

66 J Deg. 

66 £ 

Deg. 

| 

66 } Dog. 

ct 

+-> 

VI 

S 



































































































































TRAVERSE TABLE. 


49 



o 

M • 
00 
«-* 

P 

23 Deg. 

23} Deg. 

23^ 

Deg. 

23} Deg. 

O 

5T 

P 


3 

O 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

p 


51 

46.95 

19.93 

46.86 

20. 13 

46.77 

20.34 

46.68 

20.54 

51 


52 

47 8? 

20.32 

47.78 

20.53 

47.69 

20.73 

47.60 

20.94 

52 


53 

48.79 

20.71 

48.70 

20.92 

48.60 

21.13 

48.51 

21.35 

53 

1 

54 

49.71 

21.10 

49.61 

21.32 

49.52 

21.53 

49.43 

21.75 

54 


55 

50.63 

21.49 

50.53 

21.71 

50.44 

21.93 

50.34 

22.15 

55 


56 

51.55 

21.88 

51.45 

22.11 

51.36 

22.33 

51.26 

22.55 

56 


57 

52.47 

22.27 

52.37 

22.50 

52.27 

22.73 

52.17 

22.96 

57 


5S 

53.39 

22.66 

53.29 

22.90 

53.19 

23.13 

53.09 

23.36 

58 


59 

54.31 

23.05 

54.21 

23.29 

54.11 

23.53 

54 00 

23.76 

59 


66 

,55.23 

23.44 

55.13 

23.68 

55.02 

23.92 

54.92 

24.16 

60 


61 

56.15 

23.83 

56.05 

24.08 

55.91 

24.32 

55.83 

24.57 

61 


62 

57.07 

24.23 

56.97 

24 47 

56.86 

24.72 

56.75 

24.97 

62 


63 

57.99 

24.62 

57.88 

24.87 

57.77 

25.12 

57.66 

25.37 

63 


64 

58.9 L 

25.01 

58.80 

25.26 

58.69 

25.52 

58.58 

25.78 

64 


65 

59.83 

25.40 

59.72 

25.66 

59.61 

25.92 

59.50 

26.18 

65 

1 

66 

60.75 

25.79 

60.64 

26.05 

60.53 

26.32 

60.41 

26.58 

66 


67 

61.67 

26.18 

61.56 

26 • 45 

61.44 

26.72 

61.33 

26.98 

67 

■ 

68 

62.59 

26.57 

62.48 

26.84 

62.36 

27.11 

62.24 

27.39 

68 


69 

63.51 

26.96 

63.40 

27.24 

63.28 

27.51 

63.16 

27.79 

69 


70 

64.44 

27.35 

64.32 

27.63 

64.19 

27.91 

64.07 

28.19 

70 

1 

71 

65.36 

27.74 

65.23 

28.03 

65.11 

28.31 

64.99 

28.59 

71 

1 

72 

66.28 

28.13 

66.15 

28.42 

66.03 

28.71 

65.90 

29.00 

72 


73 

67.20 

28.52 

67.07 

28.82 

66.95 

29.11 

66.82 

29.40 

73 

74 

68.12 

28.91 

67.99 

29.21 

67.86 

29.51 

67.73 

29.80 

74 

j 

75 

69.04 

29.30 

68.91 

29.61 

68.78 

29.91 

68.65 

30.21 

75 


76 

69.96 

29.70 

69.83 

30.00 

69.70 

30.30 

69.56 

30.61 

76 


77 

70.88 

30.09 

70.75 

30.40 

70.61 

30.70 

70.48 

31.01 

77 

i 

78 

71.80 

30.48 

71.67 

30.79 

71.53 

31.10 

71.39 

31.41 

78 

f 

79 

72.72 

30.87 

72.58 

31.18 

72.45 

31.50 

72.31 

31.82 

79 

j 

80 

73.64 

31.26 

73.50 

31.58 

73.36 

31.90 

73.22 

32.22 

80 

81 

74.56 

31.65 

74.42 

31.97 

74.28 

32.30 

74.14 

32.62 

81 


82 

75.48 

32.04 

75.34 

32.37 

75.20 

32.70 

75.06 

33.03 

82 


83 

76.40 

32.43 

76.26 

32.76 

76.12 

33.10 

75.97 

33.43 

83 

/ 

84 

77.32 

32.82 

77.18 

33.16 

77.03 

33.49 

76.89 

33.83 

84 

'i 

85 

78.24 

33.21 

78.10 

33.55 

77.95 

33.89 

77.80 

34.23 

85 


86 

79.16 

33.60 

79.02 

33.95 

78.87 

34.29 

78.72 

34.64 

86 

\ 

87 

80.08 

33.99 

79.93 

34.34 

79.78 

34.69 

79.63 

35.04 

87 

' 

88 

81.00*1 

34.38 

80.85 

34.74 

80.70 

35.09 

80.55 

35.44 

88 


89 

81 . 92 

34.78 

81.77 

35.13 

81.62 

35.49 

81.46 

35.84 

89 

£ 

90 

82.85 

35.17 

82.69 

35.53 

82.54 

35.89 

82.38 

36.25 

90 


91 

83.77 

35.56 

83.61 

35.92 

83.45 

36.29 

83.29 

36.65 

91 


92 

84.69 

35.95 

84.53 

36.32 

84.37 

36.68 

84.21 

37.05 

92 


93 

85.61 

36.34 

85.45 

36.71 

85.29 

37.08 

85.12 

37.46 

93 

1 

94 

86.53 

36.73 

86.37 

37.11 

86.20 

37.48 

86.04 

37.86 

94 


95 

87.45 

37.12 

87.29 

37.50 

87.12 

37.88 

86 .95 

33.26 

95 

• 

96 

88.37 

37.51 

88.20 

37.90 

88.04 

38.28 

87.87 

38.66 

96 

• 

97 j 

89.29 

37.90 

89.12 

38.29 

88.95 

38.68 

88.79 

39.07 

97 


98 

90.21 

38.29 

90.04 

38.68 

89.87 

39.08 

89.70 

39.47 

98 


99 

91.13 

38.68 

90.96 

39.08 

90.79 

39.48 

90.62 

39.87 

99 

< 

100 | 

92.05 

39.07 

91.88 

39.47 

91.71 

39.87 

91.53 

40.27 

100 

l 

f 

<u 

o 

a 

I)ep. 

Lat. 

Dep. 

Lat. 

Dep 

Lat. 

Dep 

Lat. 

j Distance. 


00 
• m 

a 

67 Deg. 

66 } Deg. 

66 | Deg. 

66 } 

Deg. j 














































































































50 


TRAVERSE TABEfc, 


e 

. *— • 

p 

3 

o 

a> 

• 

24 Deg. 

24} Deg. 

24^ 

Deg. 

1 - 

24J Deg. 

— 

O 

5 

*-•• 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

o 

a 

1 

0.91 

0.41 

0.91 

0.41 

0.91 

0.41 

0.91 

0.42 

1 

2 

1.83 

0.81 

1.82 

0.82 

1.82 

0.83 

1.82 

0.84 

2 

3 

2.74 

1.22 

2.74 

1.23 

2.73 

1.24 

2 72 

1.26 

3 

4 

3.65 

1.63 

3.65 

1.64 

3.64 

1.66 

3.63 

1.67 

4 

5 

4.57 

2.03 

4.56 

2.05 

4.55 

2.07 

4.54 

2.09 

5 

6 

5.48 

2.44 

5.47 

2.46 

5.46 

2.49 

5.45 

2.51 

6 

7 

6.39 

2.85 

6.38 

2.87 

6.37 

2.90 

6.36 

2.93 

7 

1 8 

7.31 

3.25 

7.29 

3.29 

7.28 

3.32 

7.27 

3.35 

8 

9 

8.22 

3.66 

8.21 

3.70 

8.19 

3.73 

8.17 

3.77 

9 

10 

9.14 

4.07 

9.12 

4.11 

9.10 

4.15 

9.08 

4.19 

rO 

11 

10.05 

4.47 

10.03 

4.52 

10.01 

4.56 

9.99 

4.61 

11 

12 

10.96 

4.88 

10.94 

4.93 

10.92 

4.98 

10.90 

5.02 

12 

13 

11.88 

5.29 

11.85 

5.34 

11.83 

5.39 

11.81 

5.44 

13 

14 

12.79 

5.69 

12.76 

5.75 

12.74 

5.81 

12.71 

5.86 

14 

15 

13.70 

6.10 

13.68 

6.16 

13.65 

6.22 

13.62 

6.28 

15 

16 

14.62 

6.51 

14.59 

6.57 

14.56 

6.64 

14.53 

6.70 

16 

17 

15.53 

6.92 

15.50 

6.98 

15.47 

7.05 

15.44 

7.12 

17 

18 

16.44 

7.32 

16.41 

7.39 

16.38 

7.46 

16.35 

7.54 

18 

19 

j 7.36 

7.73 

17.32 

7.80 

17.29 

7.88 

17.25 

7.95 

19 

20 

18.27 

8.13 

18.24 

8.21 

18.20 

8.29 

18.16 

8.37 

20 j 

O l 

& l 

19.18 

8.54 

19.15 

8.63 

19.11 

8.71 

19.07 

8.79 

21 

22 

20.10 

8 .95 

20.06 

9.04 

20.02 

9.12 

19.98 

9.21 

22 : 

23 

21.01 

9.35 

20.97 

9.45 

20.93 

9.54 

20.89 

9.63 

23 . 

24 

21.93 

9.76 

21.88 

9.86 

21.84 

9.95 

21.80 

10.05 

24 ! 

25 

22.84 

10.17 

22.79 

10.27 

22.75 

10.37 

22.70 

10.47 

25 j 

26 

23.75 

10.58 

23.71 

10.68 

23.66 

10.78 

23.61 

10.89 

26 

27 

24.67 

10.98 

24.62 

11.09 

24.57 

11.20 

24.52 

11.30 

27 

28 

25.58 

11.39 

25.53 

11.50 

25.48 

11.61 

25.43 

11.72 

28 1 

; 29 

26.49 

11.80 

26.44 

11.91 

26.39 

12.03 

26.34 

12.14 

29 i 

30 

27.41 

12.20 

27.35 

12.32 

27.30 

12.44 

27.24 

12.56 

30 ; 

31 

28.32 

12.61 

28.26 

12.73 

28.21 

12.86 

28.15 

12.98 

31 ; 

32 

29.23 

13.02 

29.18 

13.14 

29.12 

13.27 

29.06 

13.40 

32 

33 

30.15 

13.42 

30.09 

13.55 

30.03 

13.68 

29.97 

13.82 

33 

34 

31.06 

13.83 

31.00 

13.96 

30.94 

14.10 

30.88 

14.23 

34 

35 

31.97 

14.24 

31.91 

14.38 

31.85 

14.51 

31.78 

14.65 

35 

36 

32.89 

14.64 

32.82 

14.79 

32.76 

14.93 

32.69 

15.07 

36 

37 

33.80 

15.05 

33.74 

15.20 

33.67 

15.34 

33.60 

15.49 

37 

38 

34.71 

15.46 

34.65 

15.61 

34.58 

15.76 

34.51 

15.91 

38 ‘ 

39 

35.63 

15.86 

35.56 

16.02 

35.49 

16.17 

35.42 

16.33 

39 

40 

36.54 

16.27 

36.47 

16.43 

36.40 

16.59 

36.33 

16.75 

40 

41 

37.46 

16.68 

37.38 

16.84 

37.31 

17.00 

37.23 

17.16 

41 

42 

38.37 

17.08 

38.29 

17.25 

38.22 

17.42 

38.14 

17.58 

42 

43 

39.28 

17.49 

39.21 

17.66 

39.13 

17.83 

39.05 

18.00 

43 

44 

40.20 

17.90 

40.12 

18.07 

40.04 

18.25 

39.96 

18.42 

44 

45 

41.11 

18 30 

41.03 

18.48 

40.95 

18.66 

40.87 

18.84 

45 

46 

42.02 

18.71 

41.94 

18.89 

41.86 

19.08 

41.77 

19.26 

46 . 

47 

42.94 

19.12 

42.85 

19.30 

42.77 

19.49 

42.68 

19.68 

47 

48 

43.85 

19.52 

43.76 

19.71 

43.68 

19.91 

43.59 

20.10 

48 

49 

44.76 

19.93 

44.68 

20. 13 

44.59 

20.32 

44.50 

20.51 

49 

50 

45.68 

20.34 

45.59 

20.54 

45.50 

20.73 

45.41 

20.93 

50 

| 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

§ 

l d 

( 16 
( ^ 

l 

66 Deg. 

1 

65} Deg. 

1 

65} 

1 

D".g. 

65} Deg. 

d 

•-> 

c n 

p 























































































TRAVJEHSK TABLE. 


51 


o 

V) 

r-* 

P 

24 Deg. 

24^ Deg. 

244 Deg. 

24$ De & -. 

e 

• 

cr 

c-f- 

P 

3 

o 

ra 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

a 

5 i 

46.59 

20.74 

46.50 

20.95 

46.41 

21.15 

46.32 

21.35 

~5l 

52 

47.50 

21.15 

47.41 

21.36 

47.32 

21.56 

47.22 

21.77 

52 

53 

48.42 

21.56 

48.32 

21.77 

48.23 

21.98 

48.13 

22.19 

53 

54 

49.33 

21.96 

49.24 

22.18 

49.14 

22.39 

49.04 

22.61 

54 

55 

50.24 

22.37 

50.15 

22.59 

50.05 

22.81 

49.95 

23.03 

55 

56 

i 51.16 

22.78 

51.06 

23.00 

50.96 

23.22 

50.86 

23.44 

56 

57 

52.07 

23.18 

51.97 

23.41 

! 51.87 

23.64 

51.76 

23.86 

5? 

58 

52.99 

23.59 

52.88 

23.82 

52.78 

24.05 

52.67 

24.28 

58 

59 

53.90 

24.00 

53.79 

24.23 

53.69 

24.47 

53.58 

24.70 

59 

60 

54.81 

24.40 

54.71 

24.64 

54.60 

24.88 

54.49 

25.12 

60 

61 

55.73 

24.81 

55.62 

25.05 

55.51 

25.30 

55.40 

25.54 

61 

62 

56.64 

25.22 

56.53 

25.46 

56.42 

25.71 

56.30 

25.96 

62 

63 

57.55 

25.62 

57.44 

25.88 

57.33 

26.13 

57.21 

25.38 

63 

64 

58.47 

26.03 

58.35 

26.29 

58.24 

26.54 

58.12 

26.79 

64 

65 

59.38 

26.44 

59.26 

26.70 

59.15 

26.96 

59.03 

27.21 

65 

66 

60.29 

26.84 

60.18 

27.11 

160.06 

27.37 

59. S4 

27.63 

66 

67 

61.21 

27.25 

61.09 

27.52 

;60.97 

27.78 

60.85 

28.05 

67 

68 

62.12 

27.66 

62.00 

27.93 

i61.88 

28.20 

61.75 

28.47 

68 

69 

63.03 

28.06 

62.91 

28.34 

|62.79 

28.61 

62.86 

28.89 

69 

70 

63.95 

28.47 

63.8-2 

28.75 

'63.70 

29.03 

63.57 

29.31 

70 

71 

64.86 

28.88 

64.74 

29.16 

64.61 

29.44 

64.48 

29.72 

71 

72 

65.78 

29.28 

65.65 

29.57 

65.52 

29.86 

65.39 

30.14 

72 

,73 

66.69 

29.69 

66.56 

29.98 

66.43 

30.27 

66.29 

30.56 

73 

74 

67.60 

30.10 

67.47 

30.39 

67.34 

30.69 

67.20 

30.98 

74 

75 

68.52 

30.51 

08.38 

30.80 

68.25 

31.10 

68.11 

31.40 

75 

76 

69.43 

30.91 

69.29 

31.21 

69.16 

31.52 

69.02 

31.82 

76 

77 

70.34 

31.32 

70.21 

31.63 

70.07 

31.93 

69.93 

32.24 

77 

78 

71.26 

31.73 

71.12 

32.04 

70.98 

32.35 

70.84 

32.66 

78 

79 

72.17 

32.13 

72.03 

32.45 

71.89 

32.76 

71.74 

33.07 

79 

80 

73.08 

32.54 

72.94 

32.86 

72.80 

33.18 

72.65 

33.49 

80 

81 

74.00 

32.95 

73.85 

33.27 

73.71 

33.59 

73.56 

33.91 

81 

82 

74.91 

33.35 

74.76 

33.68 

74.62 

34.00 

74.47 

34.33 

82 

83 

75.82 

33.76 

75.68 

34.09 

75.53 

34.42 

75.38 

34.75 

83 

84 

76.74 

34.17 

76.59 

34.50 

76.44 

34.83 

76.28 

35.17 

84 

85 

77.65 

34.57 

77.50 

34.91 

77.35 

35.25 

77.19 

35.59 

85 

86 

78.56 

34.98 

78.41 

35.32 

78 26 

35.66 

78.10 

36.00 

86 

87 

79.48 

35.39 

79.32 

35.73 

79.17 

36.08 

79.01 

36.42 

87 

88 

80.39 

35.79 

80.24 

36.14 

80.08 

36.49 

79.92 

36.84 

88 

89 

81.31 

36.20 

81.15 

36.55 

80. 99 

36.91 

80.82 

37 26 

89 

90 

on oc> 

O /V « /St 

36.61 

82.06 

36.96 

81.90 

37.32 

81.73 

37.68 

90 

91 

83.13 

37.01 

82.97 

37.38 

82.81 

37.74 

82.64 

33.10 

91 

92 

84.05 

37.42 

83.88 

37.79 

83.72 

38.15 

83.55 

38.52 

92 

93 i 

84.96 

37.83 

84.79 

38.20 

84.63 

38.57 

84.46 

38.94 

93 

94 

85 67 

38.23 

85.71 

38.61 

85.54 

38.98 

85.37 

39.35 

94 

95 

86 70 

38.64 

86.62 

39.02 

S6.45 

39.40 

86.27 

39 77 

95 

96 j 

87 70 

39.05 

87.53 

39.43 

87.36 

39.81 

87.18 

40.19 

96 

97 1 

88.01, 

39.45 

88.44 

39.84 

88.27 

40.23 

88.09 

40.61 

97 

98 

39.53 

39 P/3 I 

89.35 

40.25 

89.18 

40.64 

89.00 

41.03 

98 

99 

80.4.1 

40.27 

40.67 

90.26 

40.66 

90.09 

41.05 

89.91 

41.45 

99 

m 

01.35 

91. J8 

41.07 

91.00 

41.47 

90.81 

41.87 

100 

— 

V 

o 

« 

Dep. 

L?t. 

Dep. 

L<it« 

Dep. 

Lat. 

Dep. 

Lat, 

6 

c 

e 







f" 



rt 

aa 

4 

J 

63 Of" 

65f Deg. 

654 Deg. 

65 \ Deg. 

• 

Q 












































































































52 


TRAVERSE TABLE 


e 

25 Deg. 

25$ Deg. 

25i Deg 

2c} Deg. 

C? 

C* 

P 









0D 

ST 

a 

o 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

5 

a 

9 

1 

0.91 

0.42 

0.80 

0.43 i 

0.90 

0.43 

0.60 

0.43 


2 

1.81 

0.85 

1.81 

0.85 

1.81 

0.86 

1.80 

0.87 

2 

3 

2.72 

1.27 

2.71 

1.28 

2.71 

1.29 

2.70 

1.30 

3 

4 

3.63 

1.69 

3.62 

1.71 

3.61 

1.72 

3.60 

1.74 

4 

5 

4.53 

2.11 

4.52 

2.13 

4.51 

2.15 

4.50 

2.17 

5 

6 

5.44 

2.54 

5.43 

2.56 

5.42 

2.58 

5.40 

2.61 

6 

7 

6.34 

2.96 

6.33 

2.99 

6.32 

3.01 

6.30 

3.04 

7 

8 

7.25 

3.38 

7.24 

3.41 

7.22 

3.44 

7.21 

3.49 

8 

9 

8.16 

3.80 

8.14 

3.84 

8.12 

3.87 

8.11 

3.91 

9 

10 

9.06 

4.23 

9.04 

4.27 

9.03 

4.31 

9.01 

4.34 

10 

11 

9.97 

4.65 

9.95 

4.69 

9.93 

4.74 

9.91 

4.78 

11 

12 

10.88 

5.07 

10.85 

5.12 

10.83 

5.17 

10.81 

5.21 

12 

13 

11.78 

5.49 

11.76 

5.55 

11.73 

5.60 

11.71 

5.65 

13 

14 

12.b9 

5.92 

12.66 

5.97 

12.64 

6.03 

12.61 

6.08 

14 

15 

13.59 

6.34 

13.57 

6.40 

13.54 

6.46 

13.51 

6.52 

15 

16 

14.50 

6.76 

14.47 

6.83 

14.44 

6.89 

14.41 

6.95 

16 

17 

15.41 

7.18 

15.38 

7.25 

15.34 

7.32 

15.31 

7.39 

17 

18 

16.31 

7.61 

16.28 

7.68 

16.25 

7.75 

16.21 

7.82 

18 

19 

17.22 

8.03 

17.18 

8.10 

17.15 

8.18 

17.11 

8.25 

19 

20 

18.13 

8.45 

18.09 

8.53 

18.05 

8.61 

18.01 

8.69 

20 

21 

19.03 

8.87 

18.99 

8.96 

18.95 

9.04 

18.91 

9.12 

21 

22 

19.94 

9.30 

19.90 

9.38 

19.86 

9.47 

19.82 

9.56 

22 

23 

20.85 

9.72 

20.80 

9.81 

20.76 

9.90 

20.72 

9.99 

23 

24 

21 .75 

10.14 

21.71 

10.24 

21.66 

10.33 

21.62 

10.13 

24 

25 

22.66 

10.57 

22.61 

10.66 

22.56 

10.76 

22.52 

10.86 

25 

26 

23.56 

10.99 

23.52 

11.09 

23.47 

11.19 

23.42 

11.30 

26 

27 

24.47 

11.41 

24.42 

11.52 

24.37 

11.62 

24.32 

11.73 

27 

28 

25.38 

11.83 

25.32 

11.94 

25.27 

12.05 

25.22 

12.16 

28 

29 

26.28 

12.26 

26.23 

12.37 

26.17 

12.48 

26.12 

12.60 

29 

30 

27.19 

12.68 

27.13 

12.80 

27.08 

12.92 

27.02 

13.03 

30 

31 

28.10 

13.10 

28.04 

13.22 

27.98 

13.35 

27.92 

13.47 

31 

32 

29.00 

13.52 

28.94 

13.65 

28.88 

13.78 

28.82 

13.90 

32 

33 

29.91 

13.95 

29.85 

14.08 

29.79 

14.21 

29.72 

14.34 

33 

34 

30.81 

14.37 

30.75 

14.50 

30.69 

14.64 

30.62 

14.77 

34 

35 

31.72 

14.79 

31.66 

14.93 

31.59 

15.07 

31.52 

15.21 

35 

36 

32.63 

15.21 

32.56 

15.36 

32.49 

15.50 

32.43 

15.64 

36 

37 

33.53 

15.64 

33.46 

15.78 

33.40 

15.93 

33.33 

16.07 

37 

38 

34.44 

16.06 

34.37 

16.21 

34.30 

16.36 

34.23 

16.51 

38 

39 

35.35 

16.48 

35.27 

16.64 

35.20 

16.79 

35.13 

16.94 

39 

40 

36.25 

16.90 

36.18 

17.06 

36.10 

17.22 

36.03 

17.38 

40 | 

41 

37.16 

17.33 

37.08 

17.49 

37.01 

17.65 

36.93 

17.81 

41 

42 

38.06 

17.75 

37.99 

17.92 

37.91 

18.08 

37.83 

18.25 

42 

43 

38.97 

18.17 

38.89 

18.34 

38.81 

18.51 

38.73 

18.68 

43 

44 

39.88 

18.60 

39.80 

18.77 

39.71 

18.64 

39.63 

19.12 

44 

45 

40.78 

19.02 

40.70 

19.20 

40.62 

19.37 

40.53 

19.55 

45 

46 

41.69 

19.44 

41.60 

19.62 

41.52 

19.80 

41.43 

19.98 

46 

47 

42.60 

19.86 

42.51 

20.05 

42.42 

20.23 

42.33 

20.42 

1 47 

48 

43.50 

20.29 

43.41 

20.48 

43.32 

20.66 

43.23 

20.85 

| 48 

49 

44.41 

20.71 

44.32 

20.90, 

44.23 

21.10 

44.13 

21.29 

1 49 

60 

45.32 

21.13 

45.22 

21.33 

45.13 

21.63 

45.03 

21.72 

• 50 

© 

o 

a 

Dep. 

Lat. 

Dep. 

- 

Lat. 

Dep. 

Lat, 

Dep. 

Lat. 

© 

o 

c 

c3 

w 

• H 

Q 

65 Deg. 

w 

64^ Deg. 

■ 

64$ Deg. 

64$ Deg. 

sj 

LD 

• 

G 





























































































TRAVERSE TABLE 


53 


c 

S* 

r - * 

P 

25 Deg. 

25} Deg. 

25} Deg. 

25} Deg. 

& 

H • 

P 

3 

O 

® 

Lat. 

Dep. 

Lat. 

Dep. 

L&t* 

Dep. 

Lat. 

Dep. 

3 

o 

? 

51 

46.22 

21.55 

46.13 

21.75 

46.03 

21.96 

45.94 

22.16 

51 

52 

47.13 

21.98 

47.03 

22.18 

46.93 

22.39 

46.84 

22.59 

52 

53 

48.03 

22.40 

47.94 

22.61 

47.84 

22.82 

47.74 

23.03 

53 

54 

48.94 

22.82 

48.84 

23.03 

48.74 

23.25 

48.64 

23.46 

54 

55 

49.85 

23.24 

49.74 

23.46 

49.64 

23.68 

49.54 

23.89 

55 

56 

50.75 

23.67 

50.65 

23.89 

■ 50.54 

24.11 

50.44 

24.33 

56 

5^ 

51 66 

24.09 

51.55 

24.31 

51.45 

24.54 

51.34 

24.76 

57 

58 

52.57 

24.51 

52.46 

24.74 

52.35 

24.97 

52.24 

25.20 

58 

59 

53.47 

24.93 

53.36 

25.17 

53.25 

25.40 

53.14 

25.63 

59 

60 

54.38 

25.36 

54.27 

25.59 

54.16 

25.83 

54.04 

26.07 

60 

61 

55.28 

25.78 

55.17 

26.02 

55.06 

26.26 

54.94 

2 O' 1 .50 

61 

62 

56.19 

26.20 

56.08 

26.45 

55.96 

26.69 

55.84 

20.91 

69 

63 

57.10 

26.62 

56.98 

26.87 

56.86 

27.12 

56.74 

27 37 , 

63 

64 

58.00 

27.05 

57.89 

27.30 

57.77 

27.55 

57.64 

27.80 

64 

65 

58.91 

27.47 

58.79 

27.73 

58.67 

27.98 

58.55 

28.24 

65 

66 

59.82 

27.89 

59.69 

28.15 

59.57 

28.41 

59.45 

28.67 

66 

67 

60.72 

28.32 

60.60 

28.58 

60.47 

28.84 

60.35 

29.11 

67 

68 

61.63 

28.74 

61.50 

29.01 

61.38 

29.27 

61.25 

29.54 

68 

69 

62.54 

29.16 

62.41 

29.43 

62.28 

29.71 

62.15 

29.98 

69 

70 

63.44 

29.58 

63.31 

29.86 

63.18 

30.14 

63.05 

30.41 

70 

71 

64.35 

30.01 

64.22 

30.29 

64.08 

30.57 

63.95 

30.85 

71 

72 

65.25 

30.43 

65.12 

30.71 

64.99 

31.00 

64.85 

31.28 

72 

73 

66.18 

30.85 

66.03 

31.14 

65.89 

31.43 

65.75 

31.71 

73 

74 

67.07 

31.27 

66.93 

31.57 

66.79 

31.86 

66.65 

32.15 

74 

75 

67.97 

31.70 

67.83 

31.99 

67.69 

32.29 

67.55 

32.58 

75 

76 

68.88 

32.12 

68.74 

32.42 

68.60 

32.72 

68.45 

33.02 

76 

77 

69.79 

32.54 

69.64 

32.85 

69.50 

33.15 

69.35 

33.45 

77 

78 

70.69 

32.96 

70.55 

33.27 

70.40 

33.58 

70.25 

33.89 

78 

79 

71.60 

33.39 

71.45 

33.70 

71 .30 

34.01 

71.16 

34.32 

79 

80 

72.50 

33.81 

72.36 

34.13 ! 

72.21 

34.44 

72.06 

34.76 

80 

81 

73.41 

34.23 

73.26 

34.55 

73.11 

34.8/ 

72.96 

35.19 

81 

82 

74.32 

34.65 

74.17 

34.98 

74.01 

35.30 

73.86 

35.62 

82 

83 

75.22 

35.08 

75.07 

35.41 

74.91 

35.73 

74.76 

36.06 

83 

84 

76.13 

35.50 

75.97 

35.83 

75.82 

36.16 

75.66 

36.49 

84 

85 

77.04 

35.92 

76.88 

36.26 

76.72 

36.59 

76.56 

36.93 

85 

86 

77.94 

36.35 

*77.78 

36.68 

77.62 

37.02 

77.46 

37.36 

86 

87 

78.85 

36.77 

78.69 

37.11 

78.52 

37.45 

78.36 

37.80 

87 

88 

79.76 

37.19 

79.59 

37.54 

79.43 

37.88 

79.26 

38.23 

88 

89 

80.66 

37.61 

80.50 

37.96 

80.33 

38.32 

80.16 

38.67 

89 

90 

81.57 

38.04 

81.40 

38.39 

81.23 

38.75 

81.06 

39.10 

90 

91 

82.47 

38.46 

82.31 

38.82 

82.14 

39.18 

81.96 

39.53 

91 

- 92 

83.38 

38.88 

83.21 

39.24 

83.04 

39.61 

82.86 

39.97 

92 

93 

84.29 

39.30 

84.11 

39.67 

83.94 

40.04 

83.70 

40.40 

93 

94 

85.19 

39.73 

85.02 

40.10 

84.84 

40.47 

84.67 

40.84 

94 

95 

86. 10 

40.15 

85.92 

40.52 

85.75 

40.90 

85 57 

41.27 

95 

96 

87.01 

40.57 

86.83 

40.95 

86.65 

41.33 

86.47 

41.71 

96 

97 

87.91 

40.99 

87.73 

41.38 

87.55 

41.76 

87.37 

42.14 

97 

98 

88.82 

41.42 

88.64 

41.80 

!88.45 

42.19 

88.27 

42.68 

98 

99 

89.72 

41.84 

89.54 

42.23 

89.36 

42.62 

89.17 

43.01 

09 

tOO 

90.63 

42.26 

90.45 

42.66 

90.26 

43.05 

90.07 

i 43 44 

100 

© 

© 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

el 

4.1 

:J. 

Z 

_ 

ci 

CO 

o 

65 Deg. 

64f Deg. 

64i Deg. 

64} Deg. 



























































































54 


TRAVERSE 1ABLE. 


Distance.! 

26 Deg. 

26^ Deg. 

26£ Deg. 

261 Deg. 

Distance.! 

I,at. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.90 

0.44 

0.90 

0.44 

0.89 

0.45 

0.89 

0.45 

1 

2 

1.80 

9.88 

1.79 

0.88 

1.79 

0.89 

1.79 

0.90 

2 

3 

2.70 

1.32 

2.69 

1.33 

2.68 

1.34 

2.68 

1.35 

3 

4 

3.60 

1.75 

3.59 

1.77 

3.58 

1.78 

3.57 

1.80 

4 

5 

4.49 

2.19 

4.48 

2.21 

4.47 

2.23 

4.46 

2.25 

5 

6 

5.39 

2.63 

5.38 

2.65 

5.37 

2.68 

5.36 

2.70 

6 

7 

6.29 

3.07 

6.28 

3.10 

6.26 

3.12 

6.25 

3.15 

7 

8 i 

7.19 

3.51 

7.17 

3.54 

7.16 

3.57 

7.14 

3.60 

8 

9 

8.09 

3.95 

8.07 

3.98 

8.05 

4.02 

8.04 

4.05 

9 

10 

8.99 

4.38 

8.97 

4.42 

8.95 

4.46 

8.93 

4.50 

10 

11 

9.89 

4.82 

9.87 

4.87 

9.84 

4.91 

9.82 

4.95 

11 

12 

10.79 

5.26 

10.76 

5.31 

10.74 

5.35 

10.72 

5.40 

12 

13 

11.68 

5.70 

11.66 

5.75 

11.63 

5.80 

11.61 

5.85 

13 , 

14 

12.58 

6.14 

12.58 

6.19 

12.53 

6.25 

12.50 

6.30 

14 | 

15 

13.48 

6.58 

13.45 

6.63 

13.42 

6.69 

13.39 

6.75 

15 

1G 

14.38 

7.01 

14.35 

7.03 

14.32 

7.14 

14.29 

7.20 

16 

17 

15.28 

7.45 

15.25 

7.52 

15.21 

7.59 

15.18 

7.65 

17 

18 

16.18 

7.89 

16.14 

7.96 

16.11 

8.03 

16.07 

8.10 

18 

19 

17.08 

8.33 

17.04 

8.40 

17.00 

8.48 

16.97 

8.55 

19 

20 

17.98 

8.77 

17.94 

8.85 

17.90 

8.92 | 

17.86 

9. GO 

20 

21 

18.87 

9.21 

18.83 

9.29 

18.79 

9.37 

18.75 

9.45 

21 

22 

19.77 

9.64 

19.73 

9.73 

19.69 

9.82 

19.65 

9.90 

22 

23 

20.67 

10.08 

20.63 

10.17 

20.58 

10.26 

20.54 

10.35 

23 

24 

21.57 

10.52 

21.52 

10.61 

21.48 

10.71 

21.43 

10.80 

2 4 

25 

22.47 

10.96 

22.42 

11.06 

22.37 

11.15 

22.32 

1 1 .25 

25 

26 

23.37 

11.40 

23.32 

11.50 

23.27 

11.60 

23.22 

11.70 

26 

27 

24.27 

11.84 

24.22 

11.94 

24.16 

12.05 

24.11 

12.15 

27 

28 

25.17 

12.27 

25.11 

12.33 

25.06 

12.49 

25.00 

12.60 

28 

29 

26.06 

12.71 

26.01 

12.83 

25.95 

12.94 

25.90 

13.05 

29 

30 

26.96 

13.15 

26.91 

13.27 

26.85 

13.39 

26.79 

13.50 

30 

31 

27.86 

13.59 

27.80 

13.71 

27.74 

13.83 

27.63 

13.95 

31 

32 

28.76 

14.03 

28.70 

14.15 

23.64 

14.28 

28.53 

14.40 

32 

33 

29.66 

14.47 

29.60 

14.60 

29.53 

14.72 

29.47 

14.85 

33 

34 

30.56 

14.90 

30.49 

15.04 

30.43 

15.17 

30.36 

15.30 

34 

35 

31.46 

15.34 

31.39 

15.48 

31.32 

15.62 

31.25 

15.75 

35 

30 

32.36 

15.78 

32.29 

15.92 

32.22 

16.06 

32.15 

16.20 

36 

37 

33.26 

16.22 

33.18 

16.36 

33.11 

16.51 

33.04 

16.65 

37 

38 

34.15 

16.66 

34.03 

16.81 

34.01 

16.96 

33.93 

17.10 

33 

39 

35.05 

17.10 

34.98 

17.25 

34.90 

17.40 

34.83 

17.55 

39 

40 

35.95 

17.53 

35.87 

17.69 

35.80 

17.85 

35.72 

18.00 

40 

41 

36.85 

17.97 

36.77 

18.13 

36.69 

18.29 

36.61 

18.45 

41 

42 

37.75 

18.41 

37.67 

18.58 

37.59 

18.74 

37.51 

18.90 

42 

43 

38.65 

18.85 

38.57 

19.02 

3S.48 

19.19 

38.40 

19.35 

43 

44 

39.55 

19.29 

39.46 

19.46 

39.38 

19.63 

39.29 

19.80 

44 

45 

40.45 

19.73 

40.36 

19.90 

40.27 

20.08 

40.18 

20.25 

45 

46 

41.34 

20.17 

41.26 

20.35 

41.17 

20.53 

41.08 

20.70 

46 

47 

42.24 

20.60 

42.15 

20.79 

42.06 

20.97 

41.97 

21.1 5 

47 

48 

43.14 

21.04 

43.05 

21.23 

42.96 

21.42 

42.86 

21.60 

48 ' 

19 

44.04 

21.48 

43.95 

21.67 

43.85 

21.86 

43.76 

22.05 

49 

50 

j 4 ? .14 

21.92 

44.84 

22.11 

44.75 

22.31 

44.65 

22.50 

50 

$ 

c 

c 

cd 

w 

<D 

5 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i 

.a 

a 

1 

64 Deg. 

63J Deg. 

1 

63^ Deg. 

j 634 Deg. 





























































































































TRAVERSE TABLE. 


55 


“ 

►» • 
CD 
<-► 

P 

26 Dog. 

26i Deg. 

26£ 

Deg. 

26* 

Deg. 

i 

a 

K- • 

CD 

pc 

a 

o 

© 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

® 

51 

45.84 

22.36 

45.74 

22.56 

45.64 

22.76 

45 - 54 

22.96 

51 

62 

46.74 

22.80 

46.64 

23.00 

46.54 

23.20 

46.43 

23.41 

52 

53 

47.64 

23.23 

47.53 

23.44 

47.43 

23.65 

47.33 

23.88 

53 

51 

48.53 

23.67 

48.43 

23.88 

48.33 

24.09 

48 22 

24.31 

54 

55 

49.43 

24.11 

49.33 

24.33 

49.22 

24.54 

49.11 

24.76 

55 

56 

50.33 

24.55 

50.22 

24.77 

50. ] 2 

24.99 

50.01 

25.21 

56 

57 

51.23 

24.99 

51.12 

25.21 

51.01 

25-43 

50.90 

25.66 

57 

58 

52.13 

25.43 

52.02 

25.65 

51.91 

25 88 

51.79 

26.11 

53 

59 

53.03 

25.86 

52.92 

26.09 

52.80 

26.33 

52.69 

26.56 

59 

60 

53.93 

26.30 

53.81 

26.54 

53.70 

26-77 

53.58 

27.01 

60 

61 

54.83 

26.74 

54.71 

26.98 

54.59 

27.22 

54.47 

27.46 

61 

62 

55.73 

27.18 

55.61 

27.42 

5.3.49 

27.66 

55.36 

27.91 

62 

63 

56.62 

27.62 

56.50 

27.86 

56.33 

28.11 

56.26 

28.36 

63 

64 

57.52 

23.06 

57.40 

28.31 

57.28 

28.56 

57.15 

28.81 

64 

65 

53.42 

23.49 

58.30 

28.75 

58.17 

29.00 

58.04 

29.26 

65 

66 

59.32 

28.93 

59.19 

29.19 

59.07 

29.45 

58.94 

29.71 

66 

67 

60.22 

29.37 

60.09 

29.63 

59.96 

29.90 

59.83 

30.16 

67 

68 

61.12 

29.81 

60.99 

30.08 

60.86 

30.34 

60.72 

30.61 

68 

69 

62.02 

30.25 

61.88 

30.52 

61.75 

30.79 

61.62 

31.06 

69 

70 

62.92 

30.69 

62.78 

30.96 

62.65 

31.23 

62.51 

31.51 

70 

71 

63.81 

31.12 

63.68 

31.40 

63.54 

31.68 

63.40 

31.96 

71 

72 

64.71 

31.56 

64.57 

31.84 

64.44 

32.13 

64.29 

32.41 

72 

73 

65.61 

32.00 

65.47 

32.29 

65.33 

32.57 

65.19 

32.86 

73 

74 

66.51 

32.44 

66.37 

32.73 

66.23 

33.02 

66.08 

33.31 

74 

75 

67.41 

32.88 

67.27 

33.17 

67.12 

33.46 

66.97 

33.76 

75 

76 

68.31 

33.32 

68.16 

33.61 

68.01 

33.91 

67.87 

34.21 

76 

77 

69.21 

33.75 

69.06 

34.06 

68.91 

34.36 

68.76 

34.66 

77 

78 

70.11 

34.19 

69.96 

34.50 

69.80 

34.80 

69.65 

35.11 

78 

79 

71.00 

34.63 

70.85 

34.94 

70.70 

35.25 

70.55 

35.56 

79 

SO 

71.90 

35.07 

71.75 

35.38 

71.59 

35.70 

71.44 

36.01 

80 

81 

72.80 

35.51 

72.65 

35.83 

72.49 

36.14 

72.33 

36.46 

81 

82 

73.70 

35.95 

73.54 

36.27 

73.38 

36.59 

73.22 

36.91 

82 

83 

74.60 

36.38 

74.44 

36.71 

74.28 

37.03 

74.12 

37.36 

83 

84 

75.50 

36.82 

75.34 

37.15 

75.17 

37.48 

75.01 

37.81 

84 

85 

76.40 

37.26 

76.23 

37.59 

76.07 

37.93 

75.90 

38.26 

85 

86 

77.30 

37.70 

77.13 

38.04 

76.96 

38.37 

76.80 

38.71 

86 

87 

78.20 

38.14 

78.03 

38 48 

77.86 

38.82 

77.69 

39.16 

87 

88 

79.09 

38.58 

78.92 

38.92 

78.75 

39.27 

78.58 

39.61 

88 

89 

79.99 

39.01 

79.82 

39.36 

79.65 

39.71 

79.48 

40.06 

89 

90 

80.89 

39.45 

80.72 

39.81 

80.54 

40.16 

80.37 

40.51 

90 | 

'91 

81.79 

39.89 

81.62 

40.25 

81.44 

40.60 

81.26 

40.96 

91 

92 

82.69 

40.33 

82.51 

40.69 

82.33 

41.05 

82.15 

41.41 

92 

93 

83.59 

40.77 

83.41 

41.13 

83.23 

41.50 

83.05 

41.86 

93 

94 

84.49 

41.21 

84.31 

41.58 

84.12 

41.94 

83.94 

42.31 

94 

95 

85.39 

41.65 

85.20 

42.02 

85.02 

42.39 

&A-83 

42.76 

95 

96 

86.28 

42.08 

86.10 

42.46 

85.91 

42.83 

8o.73 

43.21 

96 

97 

87.18 

42.52 

87.00 

42.90 

86.81 

43.28 

86.62 

43.66 

97 

98 

88.08 

42.96 

87.89 

43.34 

87.70 

43.73 

87.51 

44.11 

98 

99 

88.98 

43.40 

88.79 

43.79 

88.60 

44.17 

88.40 

44.56 

99 

100 

89.88 

43.84 

89.69 

44.23 

89.49 

44.62 

89.30 

45.01 

100 

§ 

ss 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

8 

ci 

«-> 

00 
• H 

Q 

64 Deg. 

63| Deg. 

631 

1 

Deg. 

63i Deg. 

“a 

Q 
































































































66 


TRAVERSE TABLE 


>—< 

w 

H • 

00 

27 Deg. 

27} Deg. 

27| 

Deg. 

27} Deg. 

cc 

r*- 

P 

P 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

s 

a 

a 

] 

0.86 

0.45 

0.89 

0.46 

0.89 

j.46 


0.47 

1 

2 

1.78 

0.91 

1.78 

0.92 

1.77 

0.92 

1.77 

0.93 

2 

3 

2.67 

1.36 

2.67 

1.37 

2.66 

1.39 

2 G5 

1.40 

3 

4 

3.56 

1.82 

3.56 

1.83 

3.55 

1.85 

3.54 ! 

1.86 

4 

5 

4.4.7 I 

2.27 

4.45 

2.29 

4.44 

2.31 

4.42 

2.33 

5 

6 

o • 35 

2.72 

5.33 

2.75 

5.32 

2.77 

5.31 

2.79 

6 1 

7 

6.24 

3.18 

6.22 

3.21 

6.2J 

3.23 

6.19 

3.26 

7 

8 

7.13 

3.63 

7.11 

3.66 

7.10 

3.69 

7.08 

3.72 

8 

9 

8.02 

4.09 

8.00 

4.12 

7.98 

4.16 

7.96 

4.19 

9 

10 

8.91 | 

4.54 

8.89 

4.58 

8.87 

4.62 

8.85 

4.66 

10 

11 

9.80 

4.99 

9.78 

5.04 

9.76 

5.08 

9.73 

5.12 

11 

12 

10.69 

5.45 

10.67 

5.49 

10.64 

5.54 

10.62 

5.59 

12 

13 

11.58 

5.90 

11.56 

5.95 

11.53 

6.00 

11.50 

6.05 

13 

14 

12.47 

6.36 

12.45 

6.41 

12.42 

6.46 

12.39 

6.52 

14 

15 

13.37 

6.81 

13.34 

6.87 

13.31 

6.93 

13.27 

6.98 

15 

10 

14.26 

7.26 

14.22 

7.33 

14.19 

7.39 

14.16 

7.45 

16 

17 

15.15 

7.72 

15.11 

7.78 

15.08 

7.85 

15.04 

7.92 

17 

18 

16.04 

8.17 

16.00 

8.24 

15.97 

8.31 

15.93 

8.38 

18 

19 

16.93 

8.63 

16.89 

8.70 

16.85 

8.77 

16.81 

8.85 

19 

21) 

17.82 

9.08 

17.78 

9.16 

17.74 

9.23 

17.70 

9.31 

20 

21 

18.71 

9.53 

18.67 

9.62 

18.63 

9.70 

18.58 

9.78 

21 

22 

19.60 

9.99 

19.56 

10.07 

19.51 

10.16 

19.47 

10.24 

22 

23 

20.49 

10.44 

20.45 

10.53 

20.40 

10.62 

20.35 

10.71 

23 

24 

21.38 

10.90 

21.34 

10.99 

21.29 

11.08 

21.24 

11.17 

24 

25 

22.28 

11.35 

22.23 

11.45 

22.18 

11.54 

22.12 

11.64 

25 

26 

23.17 

11.80 

23.11 

11.90 

23.06 

12.01 

23.01 

12.11 

26 

27 

24.06 

12.26 

24.00 

12.36 

23.95 

12.47 

23.89 

12.57 

27 

28 

24.95 

12.71 

24.89 

12.82 

24.84 

12.93 

24.78 

13.04 

28 

29 

25.84 

13.17 

25.78 

13.28 

25.72 

13.39 

25.66 

13.50 

29 

30 

26.73 

13.62 

26.67 

13.74 

26.61 

13.85 

26.55 

13.97 

30 

31 

27.62 

14.07 

27.56 

14.19 

27.50 

14.31 

27.43 

14.43 

31 

32 

28.51 

14.53 

28.45 

14.65 

28.38 

14.78 

28.32 

14.90 

32 

33 

29.40 

14.98 

29.34 

15.11 

29.27 

15.24 

29.20 

15.37 

33 

34 

30.29 

15.44 

30.23 

15.57 

30.16 

15.70 

30.09 

15.83 

34 

35 

31.19 

15.89 

31.12 

16.03 

31.05 

16.16 

30.97 

16.30 

35 

36 

32.08 

16.34 

32.00 

16.48 

31.93 

16.62 

i 1.86 

16.76 

36 

37 

32.97 

16.80 

32.89 

16.94 

32.82 

17.08 

3L74 

17.23 

37 

38 

33.86 

17.25 

33.78 

17.40 

33.71 

17.55 

33.63 

17.69 

38 

39 

34.75 

17.71 

34.67 

17.86 

34.59 

18.01 

34.51 

18.16 

39 

40 

35.64 

18.16 

35.56 

18.31 

35.48 

18.47 

35.40 

18.62 

40 

41 

36.53 

118.61 

36.45 

18.77 

36.37 

18.93 

36.28 

19.09 

"41 

42 

37.42 

19.07 

37.34 

19.23 

37.25 

19.39 

37.17 

19.56 

42 

43 

38.31 

19.52 

38.23 

19.69 

38.14 

19.86 

38.05 

20.02 

43 

44 

39.20 

19.98 

39.12 

20.15 

39.03 

20.32 

38.94 

20.49 

44 

45 

40.10 

20.43 

40.01 

20.60 

39.92 

20.78 

39.82 

20.95 

45 

46 

40.99 

20.88 

40.89 

21.06 

40.80 

21.24 

40.71 

21.42 

46 

47 

41.88 

21.34 

41.78 

21.52 

41.69 

21.70 

41.59 

21.88 

47 

48 

42.77 

21.79 

42.67 

21.98 

42.58 

22.16 

42.48 

22.35 

48 

49 

43.66 

22.25 

43.56 

22.44 

43.46 

22.63 

43.36 

22.82 

49 

50 

44.55 

22.70 

44.45 

22.89 

44.35 

23.0} 

44.25 

23 28 

50 

© 

o 

a 

Dep. 

L &t« 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

Lat. 

d 

o 

c 

d 

CQ 

• 

Q 

63 Deg. 

62} Deg. 

II 

621 

Deg 

6^} Deg. 

ctf 

*-> 

CC 

5 
















































































































TRAVERSE TABLE. 


57 


a 
•— • 

OB 

«-*■ 

S» 

27 Deg. 

27} Deg. 

271 

Deg. 

27} Deg. 

C 
►— • 
to 

r-* 

3 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

3 

® 

51 

1 45.44 

23.15 

45.34 

23.35 

45.24 

23.55 

45.13 

23.75 

51 

52 

46.33 

23.61 

46.23 

23.81 

48.12 

24.01 

46.02 

24.21 

52 

53 

47.22 

24.06 

47.12 

24.27 

47.01 

24.47 

46.90 

24.68 

53 

\ 54 

48.11 

24.52 

48.01 

24.73 

47.90 

24.93 

47.79 

25.14 

54 

55 

49.01 

24.97 

48.90 

25.18 

48.79 

25.40 

48.67 

25.61 

55 

50 

49.90 

25.42 

49.78 

25.64 

49.67 

25.86 

49.56 

26.07 

56 

57 

50.79 

25.88 

50.67 

26.10 

50.56 

26.32 

50.44 

26.54 

57 

58 

51.68 

26.33 

51.56 

26.56 

51.45 

26.78 

51.33 

27.01 

58 

59 

52.57 

26.79 

52.45 

27.01 

52.33 

27.24 

52.21 

27.47 

59 

60 

53.46 

27.24 

53.34 

27.47 

53.22 

27.70 

53.10 

27.94 

60 

61 

54.35 

27.69 

54.23 

27.93 

54.11 

28.17 

53.98 

28.40 

61 

62 

55.24 

28.15 

55.12 

28.39 

54.99 

28.63 

54.87 

28.87 

62 

63 

56.13 

28.60 

56.01 

28.85 

55.88 

29.09 

55.75 

29.33 

63 

64 

57.02 

29.00 

56.90 

29.30 

56.77 

29.55 

56.64 

29.80 

64 

65 

57 92 

29.51 

57.79 

29.76 

57.66 

30.01 

57.52 

30.26 

65 

66 

58.81 

29.96 

58.68 

30.22 

58.54 

30.48 

58.41 

30.73 

66 

67 

59.70 

30.42 

59.56 

30.68 

59.43 

30.94 

59.29 

31.20 

67 

68 

!60.59 

30.87 

60.45 

31.14 

60.32 

31 .40 

60.18 

31.66 

68 

69 

61.48 

31.33 

61.34 

31.59 

61.20 

31 .86 

61.06 

32.13 

69 

70 

62.37 

31.78 

62.23 

32.05 

62.09 

32.32 

61.95 

32.59 

70 

71 

63.26 

32.23 

63.12 

32.51 

62.98 

32.78 

62.83 

33.06 

71 

7*2 

64.15 

32.69 

64.01 

32.97 

63.86 

33.25 

63.72 

33.52 

72 

1 73 

05.04 

33.14 

64.90 

33.42 

64.75 

33.71 

64.60 

33.99 

73 

J 74 

65.93 

33.60 

65.79 

33.88 

65.64 

34.17 

65.49 

34.46 

74 

I 7 » 

06.83 

34.05 

66.68 

34.34 

66.53 

34.63 

66.37 

34.92 

75 

76 

67.72 

34.50 

67.57 

34.80 

67.41 

35.09 

67.26 

35.39 

76 

77 

68.61 

34.96 

68.45 

35.26 

68.30 

35.55 

68.14 

35.85 

77 

78 

69.50 

35.41 

69.34 

35.71 

69.19 

36.02 

69.03 

36.32 

78 

79 

70.39 

35.87 

70.23 

36.17 

70.07 

36.48 

69.91 

36.78 

79 

80 

71.28 

36.32 

71.12 

36.63 

70.96 

36.94 

70.80 

37.25 

80 

81 

72.17 

36.77 

72.01 

37.09 

71.85 

37.40 

71.68 

37.71 

81 

82 

73.06 

37.23 

72.90 

37.55 

72.73 

37.86 

72.57 

38.18 

82 

83 

73.95 

37.68 

73.79 

38.00 

73.62 

38.33 

73.45 

38.65 

83 

84 

74.84 

38.14 

74.68 

38.46 

74.51 

38.79 

74.34 

39.11 

84 

85 

75.74 

38.59 

75.57 

38.92 

75.40 

39.25 

75.22 

39.58 

85 

86 

76.63 

39.04 

76.46 

39.38 

76.28 

39.71 

76.11 

40.04 

86 

87 

77.52 

39.50 

77.34 

39.83 

77.17 

40.17 

76.99 

40.51 

87 

88 

78-41 

39.95 

78.23 

40.29 

78.06 

40.63 

77.88 

40.97 

88 

89 

79.30 

40.41 

79.12 

40.75 

78.94 

41.10 

78.76 

41.44 

89 

90 

80.19 

40.86 

80.01 

41.21 

79.83 

41.56 

79.65 

41.91 

90 

91 

81.08 

41.31 

80.90 

41.67 

80.72 

42.02 

80.53 

42.37 

91 

92 

81 97 

41.77 

81.79 

42.12 

81.60 

42.48 

81.42 

42.84 

92 

93 

82.86 

42.22 

82.68 

42.58 

82.49 

42.94 

82.30 

43.30 

93 

94 

83.75 

42.68 

83.57 

43.04 

83.38 

43.40 

83.19 

43.77 

94 

95 

84.65 

43.13 

84.46 

43.50 

84.27 

43.87 

S4.07 

44.23 

95 

96 

85.54 

43.58 

85.35 

43.96 

85.15 

44.33 

84.96 

44.70 

96 

97 

86.43 

44.04 

86.23 

44.41 

86.04 

44.79 

85.84 

45.16 

97 

98 

87.32 

44.49 

87.12 

44.87 

86.93 

45.25 

86.73 

45.63 

98 

99 

88.21 

44.95 

88.01 

45.33 

87.81 

45.71 

87.61 

46.10 

99 

100 

89.10 

45.40 

88.90 

45.79 

88.70 

46.17 

88.50 

46.56 

100 

6 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

8 

a 

Ti 

M « 

5 

63 Deg. 

62} Deg. 

62} Deg. | 

I 

62} Deg. 

i 

to 

Q 












































































































58 


TRAVERSE TABLE 


Distance. 

i 

28 Deg. 

28J Deg. 

28£ 

Deg. 

28.| Deg. 

Distance. 1 
1 
1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.88 

0.47 

0.88 

0.47 

0.88 

0.48 

0.88 

0.48 

1 

, 2 

1.77 

0.94 

1.76 

0.95 

1.76 

0.95 

1.75 

0.96 

2 

3 

2.65 

1.41 

2.64 

1.42 

2.64 

1.43 

2.63 

1.44 

3 

4 

3.53 

1.88 

3.52 

1.89 

3.52 

1.91 

3.51 

1.92 

4 

5 

4.41 

2.35 

4.40 

2.37 

4.39 

2.39 

4.38 

2.40 

5 

6 

5.30 

2.82 

5.29 

2.84 

5.27 

2.86 

5.26 

2.89 

6 

7 

6.18 

3.29 

6.17 

3.31 

6.15 

3.34 

6.14 

3.37 

7 

8 

7.06 

3.76 

7.05 

3.79 

7.03 

3.82 

7.01 

3.85 

8 

9 

7.95 

4.23 

7.93 

4.26 

7.91 

4.29 

7.89 

4.33 

9 

10 

8.83 

4.69 

8.81 

4.73 

8.79 

4.77 

8.77 

4.81 

10 

11 

9.71 

5.16 

9.69 

5.21 

9.67 

5.25 

9.64 

5.29 

11 

12 

10.60 

5.63 

10.57 

5.68 

10.55 

5.73 

10.52 

5.77 

12 

13 

11.48 

6.10 

11.45 

6.15 

11.42 

6.20 

11.40 

6.25 

13 

14 

12.36 

6.57 

12.33 

6.63 

12.30 

6.68 

12.27 

6.73 

14 

15 

13.24 

7.04 

13.21 

7.10 

13.18 

7.16 

13.15 

7.21 

15 

16 

14. 13 

7.51 

14.09 

7.57 

14.06 

7.63 

14.03 

7.70 

16 

17 

15.01 

7.98 

14.98 

8.05 

14.94 

8.11 

14.90 

8.18 

17 

18 

15.89 

8.45 

15.86 

8.52 

15.82 

8.59 

15.78 

8.66 

18 

19 

16.78 

8.92 

16.74 

8.99 

16.70 

9.07 

16.66 

9.14 

19 

20 

17.66 

9.39 

17.62 

9.47 

17.58 

9.54 

17.53 

9.62 

20 

21 

18.54 

9.86 

18.50 

9.94 

18.46 

10.02 

18.41 

10.10 

21 

22 

19.42 

10.33 

19.38 

10.41 

19.33 

10.50 

19.29 

10.58 

22 

23 

20.31 

10.80 

20.26 

10.89 

20.21 

10.97 

20.16 

11.06 

23 

24 

21.19 

11.27 

21.14 

11.36 

21.09 

11.45 

21.04 

11.54 

24 

25 

22.07 

11.74 

22.02 

11.83 

21.97 

11.93 

21.92 

12.02 

25 

26 

22.96 

12.21 

22.90 

12.31 

22.85 

12.41 

22.79 

12.51 

26 

27 

23.84 

12.68 

23.78 

12.78 

23.73 

12.88 

23.67 

12.99 

27 

28 

24.72 

13.15 

24.66 

13.25 

24.61 

13.36 

24.55 

13.47 

28 

29 

25.61 

13.61 

25.55 

13.73 

25.49 

13.84 

25.43 

13.95 

29 

30 

26.49 

14.08 

26.43 

14.20 

26.36 

14.31 

26.30 

14.43 

30 

31 

27.37 

14.55 

27.31 

14.67 

27.24 

14 79 

27.18 

14.91 

31 

32 

28.25 

15.02 

28.19 

15.15 

28.12 

15 .27 

28.06 

15.39 

32 

33 

29.14 

15.49 

29.07 

15.62 

29.00 

15.75 

28.93 

15.87 

33 

34 

30.02 

15.96 

29.95 

16.09 

29.88 

16.22 

29.81 

16.35 

34 

35 

30.90 

16.43 

30.83 

16.57 

30.76 

16.70 

30.69 

16.83 

35 

36 

31.79 

16.90 

31.71 

17.04 

31.64 

17.18 

31.56 

17.32 

36 

37 

32.67 

17.37 

32.59 

17.51 

32.52 

17.65 

32.44 

17.80 

37 

38 

33.55 

17.84 

33.47 

17.99 

33.39 

18.13 

33.32 

18.28 

38 

39 

34.43 

18.31 

34.35 

18.46 

34.27 

18.61 

34.19 

18.76 

39 

40 

35.32 

18.78 

35.24 

18.93 

35.15 

19.09 

35.07 

19.24 

40 

41 

36.20 

19.25 

36.12 

19.41 

36.0-3 

19.56 

35.95 

19.72 

41 

42 

37.08 

19.72 

37.00 

19.88 

36.91 

20.04 

36.82 

20.20 

42 

43 

37.97 

20.19 

37.88 

20.35 

37.79 

20.52 

37.70 

20.68 

43 

44 

38.95 

20.66 

38.76 

20.83 

38.67 

20.99 

38.58 

21.16 

44 

45 

39.73 

21.13 

39.64 

21.30 

39.55 

21.47 

39.45 

21.64 

45 

46 

40.62 

21.60 

40.52 

21.77 

40.43 

21.95 

40.33 

22.13 

46 

47 

41.50 

22.07 

41.40 

22.25 

41.30 

22.43 

41.21 

22.61 

47 

48 

42.38 

22.53 

42.28 

22.72 

42.18 

22.90 

42.08 

23.09 

48 

49 

43.26 

23.00 

43.16 

23.19 

43.06 

23.38 

42.96 

23.57 

49 

50 

44.15 

23.47 

44.04 

23.67 

43.94 

23.86 

43.84 

24.05 

50 

© 

O 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

© 

c 

d 

-«-> 

CD 

• m 

o 

62 Deg. 

61 f Deg. 

1 

Deg. 

6H Deg. 

cti 

4-> 

XI) 

t 

Q 



































































































TRAVERSE TABLE. 


59 


e 

S’ 

r-*- 

p 

28 Deg. 

28i Deg. 

i 

28 £ Deg. 

28| Deg. 

o 

S' 

f* 

p 

B 

O 

CD 

• 

Lett. 

Dep. 

Lett* 

Dep. 

Lat. ! 

Dep. 

Lat. 

Dep. 

3 

r? 

51 

45.03 

23.94 

44.93 

24.14 

44.82 

24.34 

44.71 

24.53 

51 

52 

45.91 

24.41 

45.81 

24.61 

45.70 

24.81 

45.59 

25.01 

52 

53 

46.80 

24.88 

46.69 

25.09 

46.58 

25.29 

46.47 

25.49 

53 

54 

47.68 

25.35 

47.57 

25.56 

47.46 

25.77 

47.34 

25.97 

54 

55 

48.56 

25.82 

48.45 

26.03 

48.33 

26.24 

48.22 

26.45 

55 

66 

49.45 

26.29 

49.33 

26.51 

49.21 

26.72 

49.10 

26.94 

56 

57 

50.33 

26.76 

50.21 

26.98 

50.09 

27.20 

49.97 

27.42 

57 

58 

51.21 

27.23 

51.09 

27.45 

50.97 

27.68 

50.85 

27.90 

58 

59 

52.09 

27.70 

51.97 

27.93 1 

51.85 

28.15 

51.73 

28.38 

59 

60 

52.98 

28.17 

52.85 

28.40 | 

52.73 

28.63 

52.60 

28.86 

60 

61 

53.86 

28.64 

53.73 

23.87 

53.61 

29.11 

53.48 

29.34 

61 

62 

54.74 

29.11 

54.62 

29.35 

54.49 

29.58 

54.36 

29.82 

62 

63 

55.63 

29.58 

55.50 

29.82 

55.37 

30.06 

55.23 

30.30 

63 

64 

56.51 

30.05 

56.38 

30.29 

56.24 

30.54 

56.11 

30.78 

64 

65 

57.39 

30.52 

57.26 

30.77 

57.12 

31.02 

56.99 

31.26 

65 

66 

58.27 

30.99 

58.14 

31.24 

58.00 

31.49 

57.86 

31.75 

66 

67 

59.16 

31.45 

59.02 

31.71 

58.88 

31.97 

58.74 

32.23 

67 

68 

60.04 

31.92 

59.90 

32.19 

59.76 

32.45 

59.62 

32.71 

68 

69 

60.92 

32.39 

60.78 

32.60 

60.64 

32.92 

60.49 

33.19 

69 

70 

61.81 

32.86 

61.66 

33.13 

61.52 

33.40 

61.37 

33.67 

70 

71 

62.69 

33.33 

62.54 

33.61 

62.40 

33.88 

62.25 

34.15 

71 

72 

63.57 

33.80 

63.42 

34.08 

63.27 

34.36 

63.12 

34.63 

72 

73 

64.46 

34.27 

64.30 

34.55 

64.15 

34.83 

64.00 

35.11 

73 

74 

65.34 

34.74 

65.19 

35.03 

65.03 

35.31 

64.88 

35.59 

74 

75 

66.22 

35.21 

66.07 

35.50 

65.91 

35.79 

65.75 

36.07 

75 

76 

67.10 

35.68 

66.95 

35.97 

66.79 

36.26 

66.63 

36.56 

76 

77 

67.99 

36.15 

67.83 

36.45 

67.67 

36.74 

67.51 

37.04 

77 

78 

68.87 

36.62 

68.71 

36.92 

68.55 

37.22 

68.38 

37.52 

78 

79 

69.75 

37.09 

69.59 

37.39 

69.43 

37.70 

69.26 

38.00 

79 

80 

70.64 

37.56 

70.47 

37.87 

70.31 

38.17 

70.14 

38.48 

80 

81 

71.52 

38.03 

71.35 

38.34 

71.18 

38.65 

71.01 

33.96 

81 

82 

72.40 

38.50 

72.23 

38.81 

72.06 

39.13 

71.S9 

39.44 

82 

83 

73.28 

38.97 

73.11 

39.29 

72.94 

39.60 

172.77 

39.92 

83 

84 

74.17 

39.44 

73.99 

39.76 

73.82 

40.08 

| 73.64 

40.40 

84 

85 

75.05 

39.91 

74.88 

40.23 

74.70 

40.50 

74.52 

40.88 

85 

86 

75.93 

40.37 

75.76 

40.71 

75 58 

41.04 

75.40 

41.36 

86 

87 

76.82 

40.84 

76.64 

41.18 

76.46 

41.51 

76.28 

41.85 

87 

88 

77.70 

41.31 

77.52 

41.65 

77.34 

41.99 

77.15 

42.33 

88 

89 

78.58 

41.78 

78.40 

42.13 

78.21 

42.47 

78.03 

42.81 

89 

90 

79.47 

42.25 

79.28 

42.60 

79.09 

42.94 

78.91 

43.29 

90 

91 

80.35 

42.72 

80.16 

43.07 

79.97 

43.42 

79.78 

43.77 

91 

92 

81.23 

43.19 

81.04 

43.55 

80.85 

43.90 

80.66 

44.25 

92 

93 

82.11 

43.66 

81.92 

44.02 

81.73 

44.38 

81.54 

44.73 

93 

94 

83.00 

44.13 

82.80 

44.49 

82.61 

44.85 

82.41 

45.21 

94 

95 

83.88 

44.60 

83.68 

44.97 

83.49 

45.33 

83.29 

45.69 

95 

96 

84.78 

45.07 

84.57 

45.44 

84.37 

i45.81 

84.17 

46. 17 

96 

97 

85.65 

45.54 

85.45 

45.91 

85.25 

46.28 

85.04 

46.66 

97 

98 

86.53 

46.01 

86 33 

46.39 

86.12 

46.76 

85.92 

47.14 

98 

99 

87.41 

46.48 

87.21 

46.86 

87.00 

47.24 

86.80 

47.62 

99 

100 

88.29 

46.95 

88.09 

47.33 

87.88 

47.72 

87.67 

48.10 

100 

V 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

V 

a 

a) 

■f 

.a 

i Q 

62 Deg. 

61f Deg. 

6l£ Deg. 

6H Deg. 

cd 

at 

• »■* 

a 






















































































































60 


TRAVERSE TABLE 


1 1 

Distance. 

29 Deg. 

294 Deg. 

29i Deg. 

29f Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.87 

0.48 

0.87 

0.49 

0.87 

0.49 

0.87 

0.50 

1 

2 

1.75 

0.97 

1.74 

0.98 

1.74 

0.98 

1.74 

0.99 

2 

3 

2.62 

1.45 

2.62 

1.47 

2.61 

1.48 

2.60 

1.49 

3 

4 

3.50 

1.94 

3.49 

1.95 

3.48 

1.97 

3.47 

1.98 

4 

5 

4 37 

2.42 

4.36 

2.44 

4.35 

2.46 

4.34 

2.48 

5 

6 

5.25 

2.91 ! 

5.23 

2.93 

5.22 

2.95 

5.21 

2.98 

6 

7 

6.12 

3.39 

6.11 

3.42 

6.09 

3.45 

6.08 

3.47 

7 

8 1 

7.00 

3.88 

6.98 

3.91 

6.96 

3.94 

6.95 

3.97 

8 

9 

7.87 

4.36 

7.85 

4.40 

7.83 

4.43 

7.81 

4.47 

9 

10 

8.75 

4.85 | 

8.72 

4.89 

8.70 

4.92 

8.68 

4.90 

10 

11 

9.62 

5.33 

9.60 

5.37 

9.57 

5.42 

9.55 

5.46 

11 

12 

10.50 

5.82 

10.47 

5.86 

10.44 

5.91 

10.42 

5.95 

12 

13 

31.37 

6.30 

11.34 

6.35 

11.31 

6.40 

11.29 

6.45 

13 

14 

12.24 

6.79 

12.21 

6.84 

12.18 

6.89 

12.15 

6.95 

14 

15 

13.12 

7.27 

13.09 

7.33 

13.06 

7.39 

13.02 

7.44 

15 

16 

13.99 

7.76 

13.96 

7.82 

13.93 

7.88 

13.89 

7.94 

16 

17 

14.87 

8.24 

14.83 

8.31 

14.80 

8.37 

14.76 

8.44 

17 

18 

15.74 

8.73 

15.70 

8.80 

15.67 

8.86 

15.63 

8.93 

18 

19 

16.62 

9.21 

16.58 

9.28 

16.54 

9.36 

16.50 

9.43 

19 

20 

17.49 

9.70 

17.45 

9.77 

17.41 

9.85 

17.36 

9.92 

20 

21 

18.37 

10.18 

18.32 

10.26 

18.28 

10.34 

18.23 

10.42 

21 

22 

19.24 

10.67 

19.19 

10.75 

19.15 

10.83 

19.10 

10.92 

22 

23 

20.12 

11.15 

20.07 

11.24 

20.02 

11.33 

19.97 

11.41 

23 

24 

20.99 

11.64 

20.94 

11.73 

20.89 

11.82 

20.84 

11.91 

24 

25 

21.87 

12.12 

21.81 

12.22 

21.76 

12.31 

21.70 

12.41 

25 

26 

22.74 

12.60 

22.68 

12.70 

22.63 

12.80 

22.57 

12.90 

26 

27 

23.61 

13.09 

23.56 

13.19 

23.50 

13.30 

23.44 

13.40 

27 

28 

24.49 

13.57 

24.43 

13.68 

24.37 

13.79 

24.31 

13.89 

28 

29 

25.36 

14.06 

25.30 

14.17 

25.24 

14.28 

25.18 

14.39 

29 

30 

26.24 

14.54 

20.17 

14.66 

26.11 

14.77 

26.05 

14.89 

30 

31 

27.11 

15.03 

27.05 

15.15 

26.98 

15.27 

26.91 

15.38 

31 

32 

27.99 

15.51 

27.92 

15.64 

27.85 

15.76 

27.78 

15.88 

32 

33 

28.86 

16.00 

28.79 

16.12 

28.72 

16.25 

28.65 

16.38 

33 

34 

29.74 

16.48 

29.66 

16.61 

29.59 

16.74 

29.52 

16.87 

34 

35 

30.61 

16.97 

30.54 

17.10 

30.46 

17.23 

30.39 

17.37 

35 

36 

31.49 

17.45 

31.41 

17.59 

31.33 

17.73 

31.26 

17.86 

36 

37 

32.36 

17.94 

32.28 

18.08 

32.20 

18.22 

32.12 

18.36 

37 

38 

33.24 

18.42 

33.15 

18.57 

33.07 

18.71 

32.99 

18.86 

38 

39 

34.11 

18.91 

34.03 

19.06 

33.94 

19.20 

33.86 

19.35 

39 

40 

34.98 

19.39 

34.90 

19.54 

34.81 

19.70 

34.73 

19.85 

40 

41 

35.86 

19.88 

35.77 

20.03 

35.68 

20.19 

35.60 

20.34 

41 

42 

36.73 

20.36 

36.64 

20.52 

36.55 

20.68 

36.46 

20.84 

42 

43 

37.61 

20.85 

37.52 

21.01 

37.43 

21.17 

37.33 

21.34 

43 

44 

38.48 

21.33 

38.39 

21.50 

38.30 

21.67 

38.20 

21.83 

44 

45 

39.36 

21.82 

39.26 

21.99 

39.17 

22.16 

39.07 

22.33 

45 

46 

40.23 

22.30 

40.13 

22.48 

40.04 

22.65 

39.94 

22.83 

46 

47 

41.11 

22.79 

41.01 

22.97 

40.91 

23.14 

40.81 

23.32 

47 

48 

41.98 

23.27 

41.88 

23.45 

41.78 

23.68 

41 .67 

23.82 

48 

49 

42.86 

23.76 

42.75 

23.94 

42.65 

24.13 

42.54 

24.31 

49 

60 

J3.73 

24.24 

43.62 

24.43 

43.52 

24.62 

43.41 

24.81 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

o 

c 

61 

1 

Deg. 

60f Deg. 

60$ Deg. 

60$ Deg. 

rt 

.2 

Q 





























































































































TRAVERSE TABLE 


61 


w» 

y 

vn 

t-+ 

p 

aa Deg. 

29} Deg. 

29j 

Deg. 

29| Deg. 

~1 

O 

w 

r**“ 

P 

3 

O ' 
p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

a 

61 

44.61 

24.73 

44.50 

24.92 

44.39 

25.11 

44.28 

25.31 

51 

52 

45.48 

25.21 

45.37 

25.41 

45.26 

25.61 

45.15 

25.80 

52 

53 

46.35 

25.69 

46.24 

25.90 

46.13 

26.10 

46.01 

26.30 

51 f 

54 

47.23 

26.18 

47.11 

26.39 

47.00 

26.59 

46.88 

26.80 

54 

55 

48.10 

26.66 

47.99 

26.87 

47.87 

27.08 

47.75 

27.29 

55 

50 

48.98 

27.15 

48.80 

27.36 

48.74 

27.58 

48.62 

27.79 

561 

57 

49.85 

27.63 

49.73 

27.85 

49.61 

28.07 

49.49 

28.28 

57 

58 

50.73 

28.12 

50.60 

28.34 

50.48 

28.56 

50.36 

28.78 

58 

59 

51.60 

28.60 

51.48 

28.83 

51.35 

29.05 

51.22 

29.28 

59 

60 

52.48 

29.09 

52.35 

29.32 

52.22 

29.55 

52.09 

29.77 

60 

61 

53.35 

29.57 

53.22 

29.81 

53.09 

30.04 

52.96 

30.27 

61 

62 

54.23 

30.06 

54.09 

30.29 

53.96 

30.53 

53.83 

30.77 

62 

63 

55.10 

30.54 

54.97 

30.78 

54.83 

31.02 

54.70 

31 .26 

63 

64 

55.98 

31.03 

55.84 

31.27 

55.70 

31.52 

55.56 

31 .76 

64 

65 

56.85 

31.51 

56.71 

31.76 

56.57 

32.01 

58.43 

32.25 

65 

66 

57.72 

32.00 

57.58 

32.25 

57.44 

32.50 

57.30 

32.75 

66 

67 

58.60 

32.48 

58.46 

32.74 

58.31 

32.99 

58.17 

33.25 

67 

68 

59.47 

32.97 

59.33 

33.23 

59.18 

33.48 

59.04 

33.74 

68 

69 

60.35 

33.45 

60.20 

33.71 

60.05 

33.98 

59.91 

34.24 

69 J 

70 

61.22 

33.94 

61.07 

34.20 

00.92 

34.47 

60.77 

34.74 

70 

71 

62.10 

34.42 

61.95 

34.69 

61.80 

34.96 

61 .64 

35.23 

71 

72 

62.97 

34.91 

62.82 

35.18 

62.67 

35.45 

62.51 

35.73 

72 

73 

63.85 

35.39 

63.69 

35.67 

63.54 

35.95 

63.38 

36.22 

73 

74 

64.72 

35.88 

64.56 

36.16 

64.41 

30.44 

64.25 

36.72 

74 

75 

65.60 

36.36 

65.44 

36.65 

65.28 

36.93 

65.1 l 

37.22 

75 

76 

66.47 

36.85 

66.31 

37.14 

66.15 

37.42 

65.98 

37.71 

76 

77 

67.35 

37.33 

07.18 

37.62 

67.02 

37.92 

66.85 

38.21 

77 

78 

68.22 

37.82 

68.05 

38.11 

67.89 

38.41 

67.72 

38.70 

78 

79 

69.09 

38.30 

68.93 

38.60 

68.76 

38.90 

68.59 

39.20 

79 

80 

69.97 

38.78 

69.80 

39.09 

69.63 

39.39 

69.46 

39.70 

80 

81 

70.84 

39.27 

70.67 

39.58 

70.50 

39.89 

70.32 

40.19 

81 

82 

71.72 

39.75 

71.54 

40.07 

71.37 

40.38 

71.19 

40.69 

82 1 

83 

72.59 

40.24 

72.42 

40.56 

72.24 

40.87 

72.06 

41.19 

83 

84 

73.47 

40.72 

73.29 

41.04 

73.11 

41.36 

72.93 

41.68 

84 

85 

74.34 

41.21 

74.16 

41.53 

73.98 

41.86 

73.80 

42.18 

85 

86 

75.22 

41.69 

75.03 

42.02 

| 74.85 

42.35 

74.67 

42.67 

86 

87 

76.09 

42.18 

75.91 

42.51 

75.72 

42.84 

75.53 

43.17 

87 

88 

76.97 

42.65 

76.78 

43.00 

76.59 

43.33 

76.40 

43.67 

88 

89 

77.84 

43.15 

77.65 

43.49 

77.46 

43.83 

77.27 

44.16 

89 

90 

78.72 

43.63 

78.52 

43.98 

78.33 

44.32 

78.14 

44.66 

90 

91 

79.59 

44.12 

79.40 

44.46 

79.20 

44.8.1 

79.01 

45.16 

91 

92 

80.46 

44.60 

80.27 

44.95 

SO. 07 

45.30 

79.87 

45.65 

92 

93 

81.34 

45.09 

81.14 

45.44 

SO.94 

45.80 

80.74 

46.15 

93 

94 

82.21 

45.57 

82.01 

45.93 

81.81 

46.29 

81.61 

46.64 

94 

95 

83.09 

46.06 

82.89 

46.42 

82.68 

46.78 

82.48 

47.14 

95 

96 

8.7.96 

46.54 

83.76 

46.91 

83.55 

47.27 

83.35 

47.64 

9b 

97 

84.84 

47.03 

84.63 

47.40 

84.42 

47.77 

84.22 

48.13 

97 

98 

85.71 

47.51 

85.50 

47.88 

85.29 

48.26 

85.08 

48.63 

98 1 

99 

80.59 

48.00 

86.38 

48.31 

S6.17 

48.75 

85.95 

49.13 

99 

100 

87.46 

48.48 

87.25 

48.86 

87.04 

49.24 

86.82 

49.62 

100 

© 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

V 1 

V 

c 

cd 

*-» 

1 ® 

, . —4 

1° 

) 

2 

2 

1 ° 

61 Deg. 

i 

60| Deg. 

60i 

Deg. 

60} Deg. 


23 










































































































62 


TRAVERSE TABLE. 


Distance. 

30 Deg. 

30^ Deg. 

30^ 

Deg. 

303 Deg’ 

© 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

? 

1 

0.87 

0.50 

0.81 

0.50 

0.86 

0.51 

0.86 

0.51 

T 

2 

1.73 

1.00 

1.73 

1.01 

1.72 

1.02 

1.72 

1.02 

2 

3 

2.60 

1.50 

2 59 

1.51 

2.58 1 

1.52 

2 58 

1.53 

3 

4 

3.46 

2.00 

3.46 

2.02 

3.45 

2.03 

3 .44 

2.05 

4 

5 

4.33 

2.50 

4.32 

2.52 

4.31 

2.54 

4 30 

2.56 

5 

6 

5.20 

3.00 

5.18 

3.02 

5.17 

3.05 

5.16 

3.07 

6 

7 

6.06 

3.50 

6.05 

3.53 

6.03 

3.55 

6.02 

3.58 

7 

8 

6.93 

4.00 

6.91 

4.03 

6.89 

4.06 

6.88 

4.09 

8 

9 

7.79 

4.50 

7.77 

4.53 

7.75 

4.57 

7.73 

4.60 

9 

10 

8.66 

5.00 

8.64 

5.04 

8.62 

5.08 

8.59 

5.11 

. 9 

11 

9.53 

5.50 

9.50 

5.54 

9.48 

5.58 

9.45 

5.62 

: i 

12 

10.39 

6.00 

10.37 

6.05 

10.34 

6.09 1 

10.31 

6.14 

12 

13 

11.26 

6.50 

11.23 

6.55 

11.20 

6.60 

11.17 

6.65 

13 

14 

12.12 

7.00 

12.09 

7.05 

12.06 

7.11 1 

12.03 

7.16 

11 

15 

12.99 

7.50 

12.96 

7.56 

12.92 

7.61 

12.89 

7.67 

1 5 

16 

13.86 

8.00 

13.82 

8.06 

13.79 

8.12 

13.75 

8.18 

16 

17 

14.72 

8.50 

14.69 

8.56 

14.65 

8.63 

14.61 

8.69 

17 

18 

15.59 

9.00 

15.55 

9.07 

15.51 

9.14 

15.47 

9.20 

18 

19 

16.45 

9.50 

16.41 

9.57 

16.37 

9.64 

16.33 

9.71 

19 

20 

17.32 

10.00 

17.28 

10.08 

17.23 

10.15 

17.19 

10.23 

20 

21 

18.19 

10.50 

18.14 

10.58 

18.09 

10.66 

18.05 

10.74 

21 

22 

19.05 

11.00 

19.00 

11.08 

18.96 

11.17 

18.91 

11.25 

22 

23 

19.92 

11.50 

19.87 

11.59 

19.82 

11.67 

19.77 

11.76 

23 

24 

20.78 

12.00 

20.73 

12.09 

20.68 

12.18 

20.63 

12.27 

24 

25 

21.65 

12.50 

21.60 

12.59 

21.54 

12.69 

21.49 

12.78 

25 

26 

22.52 

13.00 

22.46 

13.10 

22.40 

13.20 

22.34 

13.29 

26 

27 

23.38 

13.50 

23.32 

13.60 

23.26 

13.70 

23.20 

13.80 

27 

28 

24.25 

14.00 

24.19 

14.11 

24.13 

14.21 

24.06 

14.32 

28 

29 

25.11 

14.50 

25.05 

14.61 

24.99 

14.72 

24.92 

14.83 

29 

30 

25.98 

15.00 

25.92 

15.11 

25.85 

15.23 

25.78 

15.34 

30 

31 

26.85 

15.50 

26.78 

15.62 

26.71 

15.73 

26.64 

15.85 

'31 

32 

27.71 

16.00 

27.64 

16.12 

27.57 

16.24 

27.50 

16.36 

32 

33 

28.58 

16.50 

28.51 

16.62 

28.43 

16.75 

28.36 

16.87 

33 

34 

29.44 

17.00 

29.37 

17.13 

29.30 

17.26 

29.22 

17.38 

34 

35 

30.31 

17.50 

30.23 

17.63 

30.16 

17.76 

30.08 

17.90 

35 

36 

31.18 

18.00 

31.10 

18.14 

31.02 

18.27 

30.94 

18.41 

36 

37 

32.04 

18.50 

31.96 

18.64 

31.88 

18.78 

31.80 

18.92 

37 

38 

32.91 

19.00 

32.83 

19.14 

32.74 

19.29 

32.66 

19.43 

38 

39 

33.77 

19.50 

33.69 

19.65 

33.60 

19.79 

33.52 

19.94 

39 

40 

34.64 

20.00 

34.55 

20.15 

34.47 

20.30 

34.38 

20.45 

40 

41 

35.51 

20.50 

35.42 

20.65 

35.33 

20.81 

35.24 

20.96 

41 

42 

36.37 

21.00 

36.28 

21.16 

36.19 

21.32 

36.10 

21.47 

42 

43 

37.24 

21.50 

37.14 

21.66 

37.05 

21.82 

36.95 

21.99 

43 

44 

38.11 

22.00 

38.01 

22.17 

37.91 

22.33 

37.81 

22.50 

44 

45 

38.97 

22.50 

38.87 

22.67 

38.77 

22.84 

38.67 I 23.01 

45 

48 

39.84 

23.00 

39.74 

23.17 

39.63 

23.35 

39.53 

23.52 

4 ? 

47 

40.70 

23.50 

40.60 

23.68 

40.50 

23.85 

40.39 

24.03 

45 j 

48 

41.57 

24.00 

41.46 

24.18 

41.36 

24.36 

41.25 

24.54 

46 

49 

42.44 

24.50 

42.33 

24.68 

42.22 

24.87 

42.11 

25.05 

49 

50 

43.30 

25.00 

43.19 

25.19 

43.08 

25.38 

42.97 

j 25.56 

50 

© 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

h 

csJ 

w 

W 

5 

60 Deg. 

59f Deg. 

59.\ Deg. 

59} Deg. 

ri 

V; 

i 2 

j — \ 












































































































TRAVERSE TAItLE 


63 


e 

00 

p 

<t 

30 Deg. 

30^ Deg. 

30^ Deg. 

30} 

Deg. 

Distance. 

Lai. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

j Lat. 

Dep. 

51 

44.17 

25.50 

44.06 

25.69 

43.94 

25.88 li 43.83 

26.08 

; 51 

52 

45.03 

26.00 

44.92 

26.20 

44.80 

26.39 

144.69 

26.59 

52 

53 

45.90 

26.50 

45.78 

26.70 

45.67 

26.90 

;45.55 

27.10 

53 

54 

46.77 

27.00 

46.65 

27.20 

46.53 

27.41 

46.41 

27.61 

54 

55 

47.63 

27.50 

47.51 

27.71 

47.39 

27.91 

47.27 

28.12 

55 

56 

48.50 

28.00 

48.37 

28.21 

48.25 

28.42 

48.13 

28.63 

56 

57 

49.36 

28.50 

49.24 

28.72 

49.11 

28 93 

48.99 

29.14 

S7\ 

58 

50 23 

29.00 

50.10 

29.22 

49.97 

29.44 

49.85 

29.65 

58 

59 

51.10 

29.50 

50.97 

29.72 

50.84 

29.94 

50.70 

30.17 

59 

1 60 

51.96 

30.00 

51.83 

30.23 

51.70 

30.45 

51.56 

30.68 

60 

61 

52.83 

30.50 

52.69 

30.73 

‘52.56 

30.96 

52.42 

31.19 

61 

62 

53.69 

31.00 

53.56 

31.23 

53.42 

31.47 

53.28 

31.70 

62 

| 63 

54.56 

31.50 

54.42 

31.74 

54.28 

31.97 

54.14 

32.21 

63 

| 64 

55.43 

32.00 

55.29 

32.24 

55.14 

32.48 

55.00 

32.72 

64 

65 

56.29 

32.50 

56.15 

32.75 

56.01 

32.99 

55.86 

33.23 

65 

| 66 

57.16 

33.00 

57.01 

33.25 

56.87 

33.50 

56.72 

33.75 

66 

! 67 

58.02 

33.50 

57.88 

33.75 

t>7.73 

34.01 

57.58 

34.26 

67 

i 68 

58.89 

34.00 

58.74 

34.26 

58.59 

34.51 

58.44 

34.77 

68 

; 69 

59.76 

34.50 

59.60 

34.76 

59.45 

35.02 

59.30 

35.28 

69 

j 70 

60.62 

35.00 

60.47 

35.26 

60.31 

35.53 

60.16 

35.79 

70 

! 71 

61.49 

35,50 

61.33 

35.77 

61.18 

36.04 

61.02 

36.30 

71 

72 

62.35 

36.00 

62.20 

36.27 

62.04 

36.54 

61.88 

36.81 

72 

i 73 

63.22 

36.50 

63.06 

36.78 

62.90 

37.05 

62.74 

37.32 

73 

74 

64.09 

37.00 

63.92 

37.28 

63.76 

37.56 

63.60 

37.84 

74 

i 75 

64.95 

37.50 

64.79 

37.78 

64.62 

38.07 

64.46 

38.35 

75 

7-6 

65.82 

38.00 

65.65 

33.29 

65.48 

38.57 

65.31 

38.86 

76 

77 

66.68 

38.50 

66.52 

38.79 

66.35 

39.08 

66.17 

39.37 

77 

78 

67.55 

39.00 

67.3S 

39.29 

67.21 

39.59 

67.03 

39.88 

78 

79 

68.42 

39.50 

68.24 

39.80 

68.07 

40.10 

67.89 

40.39 

79 

80 

69.28 

40.00 

69.11 

40.30 

68.93 

40.60 

68.75 

40.90 

80 

81 

70.15 

40.50 

69.97 

40.81 

69.79 

41.11 

69.61 

41.41 

81 

82 

71.01 

41.00 

70.83 

41.31 

70.65 

41.62 

70.47 

41.93 

82 

83 

71.88 

41.50 

71.70 

41.81 

71.52 

42.13 

71.33 

42.44 

83 

! 84 

72.75 

42.00 

72.56 

42.32 

72.38 

42.63 

72.19 

42.95 

84 

j 85 

73.61 

42.50 

73.43 

42.82 

73.24 

43.14 

73.05 

43.46 

85 

i 86 

74.48 

43.00 

74.29 

43.32 

74.10 

43.65 

73.91 

43.97 

86 

j 87 

75.34 

43.50 

75.15 

43.83 

74.96 

44.16 

74.77 

44.48 

87 

j 88 

76.21 

44.00 

76.02 

44.33 

75.82 

44.66 

75.63 

44.89 

88 

! 89 

77.08 

44.50 

76.88 

44.84 

76.68 

45.17 

76.49 

45.51 

89 

1 90 

77.94 

45.00 

77.75 

45.34 

77.55 

45.68 

77.35 

46.02 

90 

91 

78.81 

45.50 

78.61 

45.84 

78.41 

46.19 

78.21 

46.53 

91 

92 

79.67 

46.00 

79.47 

46.35 

79.27 

46.69 

79.07 

47.04 

92 

93 

80.54 

46.50 

80.34 

46.85 

80.13 

47.20 

79.92 

47.55 

93 

94 

81.41 

47.00 

81.20 

47.35 

80.99 

47.71 

80.78 

48.06 

94 

95 

82.27 

47.50 

82.06 

47.86 

81.85 

48.22 

81.64 

48.57 

95 

96 

83.14 

48.00 

82.93 

48.36 

82.72 

48.72 

82.50 

49.08 

96 

97 

84.00 

48.50 

83.79 

48.87 

83.58 

49.23 

83.36 

49.60 

97 

98 

84.87 

49.00 

84.66 

49.37 1 

84.44 

49.74 

84.22 

50.11 

98 

99 

85.74 

49.50 

85.52 

49.87 

85.30 

50.25 

85.08 

50.62 

99 

100 

86.60 

50.00 

86.38 

50.38 

86.16 

50.75 

85.94 

51.13 

100 

6 

<J 

c 

Dep. 

Lat. 

Dep. 

Lat. 

II 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

c : 

rf 

«-> 

00 
• —* 

C) 

1 

60 Deg. 

59| Deg. 

1 

59£ Deg. 

i 

59£ Deg. 

ci 

•*-> 

•/} 

o 














































































































04 


TRAVERSE TABLE 


g 

S’ 

31 Deg. 

31} Deg. 

31 } Deg. 

31} Deg. 

- 

3 

GO 

3 

rt 

® 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

»-* 

O 

CD 

• 

1 

0.86 

0.51 

0.85 

0.52 

0.85 

0.52 

0.85 

0.53 

1 

2 

1.71 

1.03 

1.71 

1.04 

1.71 

1.04 

1.70 

1.05 

2 

a 

2.57 

1.55 

2.56 

1.56 

2.56 

1.57 

2.55 

1.58 

3 

4,- 

5 

3.43 

2.06 

3.42 

2.08 

3.41 

2.09 

3.40 

2.10 

4 

4.29 

2.58 

4.27 

2.59 

4.26 

2.61 

4.25 

2.63 

5 

e 

5.14 

3.09 

5.13 

3.11 

5.12 

3.13 

5.10 

3.16 

6 

7 

6.00 

3.61 

5.98 

3.63 

5.97 

3.66 

5.95 

3.63 

7 

8 

6.86 

4.12 

6.84 

4.15 

6.82 

4.18 

6.80 

4.21 

8 

9 

7.71 

4.64 

7.09 

4.67 

7.67 

4.70 

7.65 

4.74 

9 

10 

8.57 

5.15 

8.55 

5.19 

8.53 

5.22 

8.50 

5.26 

10 ' 

11 

9 43 

5.67 

9.40 

5.71 

9.38 

5.75 

9.35 

5.79 

ii 

12 

10.29 

6.18 

10.26 

6.23 

10.23 

6.27 

10.20 

6.31 

12 

13 

11.14 

6.70 

11.11 

6.74 

11.08 

6.79 

11.05 

6.84 

13 

14 

12.00 

7.21 

11.97 

7.26 

11.94 

7.31 

11.90 

7.37 

14 

15 

12.86 

7.73 

12.82 

7.78 

12.79 

7.84 

12.76 

7.89 

15 

16 

13.71 

8.24 

13.68 

8.30 

13.64 

8.36 

13.61 

8.42 

16 

17 

14.57 

8.76 

14.53 

8.82 

14.49 

8.88 

14.46 

8.95 

17 

18 

15.43 

9.27 

15.39 

9.34 

15.35 

9.40 

15.31 

9.47 

18 

19 

16.29 

9.79 

16.24 

9.86 

16.20 

9.93 

16.16 

10.00 

19 

20 

17.14 

10.30 

17.10 

10.38 

17.05 

10.45 

17.01 

10.52 

20 

21 

18.00 

10.82 

17.95 

10.89 

17.91 

10.97 

17.86 

11.05 

21 

22 

18.86 

11.33 

18.81 

11.41 

18.76 

11.49 

18.71 

11.58 

22 

23 

19.71 

11.85 

19.66 

11.93 

19.61 

12.02 

19.56 

12.10 

23 

24 

20.57 

12.36 

20.52 

12.45 

20.46 

12.54 

20.41 

12.63 

24 

25 

21.43 

12.88 

21.37 

12.97 

21.32 

13.06 

121.26 

13.16 

25 

26 

22.29 

13.39 

22.23 

13.49 

22.17 

13.58 

i22.11 

13.68 

26 

27 

23.14 

13.91 

23.03 

14.01 

23.02 

14.11 

[22.96 

14.21 

27 

28 

24.00 

14.42 

23.94 

14.53 

23.87 

14.63 

23.81 

14.73 

28 

29 

24.86 

14.94 

24.79 

15.04 

24.73 

15.15 

24.66 

15.26 

29 

30 

25.71 

15.45 

25.65 

15.56 

25.58 

15.67 

25.51 

15.79 

30 

31 

26.57 

15.97 

26.50 

16.08 

26.43 

16.20 

26.36 

16.31 

31 

32 

27.43 

16.48 

27.36 

16.00 

27.28 

16.72 

27.21 

16.84 

32 

33 

28.29 

17.00 

28.21 

17.12 

28.14 

17.24 

28.06 

17.37 

33 

34 

29.14 

17.51 

29.07 

17.64 

28.99 

17.76 

128.91 

17.89 

34 

35 

30.00 

18.03 

29.92 

18.16 

29.84 

18.29 

29.76 

18.42 

35 

36 

30.86 

18.54 

30.78 

18.68 

30.70 

18.81 

30.61 

18.94 

36 

37 

31.72 

19.06 

31.63 

19.19 

31.55 

19.33 

31.46 

19.47 

37 

38 

32.57 

19.57 

32.49 

19.71 

32.40 

19.85 

32.31 

20.00 

38 

39 

33.43 

20.09 

33.34 

20.23 

33.25 

20.38 

33.16 

20.52 

39 

40 

34.29 

20.60 

34.20 

20.75 

34.11 

20.90 

34.01 

21 05 

40 

41 

35.14 

21.12 

35.05 

21.27 

34.96 

21.42 

34.86 

21.57 

41 

42 

36.00 

21.63 

35.91 

21.79 

35.81 

21.94 

35.71 

22.10 

42 

43 

36.86 

22.15 

36.76 

22.31 

36.66 

22.47 

36.57 

22.63 

43 

44 

37.72 

22.66 

37.62 

22.83 

37.52 

22.99 

j 37.42 
38.27 

23.15 

41 

45 

38.57 

23.18 

38.47 

23.34 

38.37 

23.51 

23.68 

45 

46 

39.43 

23.69 

39.33 

23.86 

39.22 

24.03 

|39.12 

24.21 

46 

47 

40.29 

24.21 

40.18 

24.38 

40.07 

24.56 

,39.97 

24.73 

47 

48 

41.14 

24.72 

41 04 

24.90 

40.93 

25.08 

40.82 

25.26 

48 

49 

42.00 

25.24 

41.89 

25.42 

41.78 

25.60 

41.67 

25.78 

49 

50 

42.86 

25.75 

42.75 

25.94 

42.63 

26.12 

42.52 

26.31 

50 

6 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

al 

o 

C 

CO 

• H 

Q 

59 Deg. 

58| Deg. 

58} Deg. 

58} Deg, 

cd 

■*-> 

m 

• 

r-f 













































































































TRAVERSE TABLE 


65 


• 

7> 

P 

31 Deg. 

31$ Deg. 

3ii 

Deg. 

31$ Deg. 

O 

5* 

«-* 

p 

3 

r: 

cc 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

CD 

51 

43.72 

26.27 

43.60 

26.46 

43.48 

26.65 

43.37 

26.84 

5i 

52 

44.57 

26.78 

44.46 

26.98 

44.34 

27.17 

44.22 

27.36 

52 

53 

45.43 

27.30 

45.31 

27.49 

45.19 

27.69 

45.07 

27.89 

53 

54 

46.29 

27.81 

46.17 

28.01 

46.04 

28.21 

45.92 

28.42 

54 

55 

47.14 

28.33 

47.02 

28.53 

46.90 

28.74 

46,77 

28.94 

55* 

56 

48.00 

28.84 

47.88 

29.05 

47.75 

29.26 

47.62 

29.47 

56 

5? 

48.86 

29.36 

48.73 

29.57 

48.60 

29.78 

48.47 

29.99 

57 

58 

49.72 

29.87 

49.58 

30.09 

49.45 

30.30 

49.32 

30.52 

59 

59 

50.57 

30.39 

50 44 

30.61 

50.31 

30.83 

50.17 

31.05 

59 

60 

51.43 

30.90 

51.29 

31.13 

51.16 

31.35 

51.02 

31.57 

60 i 

61 

52.29 

31.42 

52.15 

31.65 

52.01 

31.87 

51.87 

32.10 

61 

62 

53.14 

31.93 

53.00 

32.16 

52.86 

32.39 

52.72 

32.63 

62 

63 

54.00 

32.45 

53.86 

32.68 

53.72 

32.92 

53.57 

33.15 

63 

64 

54.86 

32.96 

54.71 

33.20 

54.57 

33.44 

54.42 

33.68 

64 

65 

55.72 

33.48 

55.57 

33.72 

55.42 

33.96 

55.27 

34.20 

65 

66 

56.57 

33.99 

56.42 

34.24 

56.27 

34.48 

56.12 

34.73 

66 

67 

57.43 

34.51 

57.28 

34.76 

57.13 

35.01 

56.98 

35.26 

67 

68 

58.29 

35.02 

58.13 

35.28 

57.98 

35.53 

57.82 

35.78 

68 

69 

59.14 

35.54 

58.99 

35.80 

58.83 

36.05 

58.67 

36.31 

69 

70 

60.00 

36.05 

59.84 

36.31 

59.68 

36.57 

59.52 

36.83 

70 

71 

60.86 

36.57 

60.70 

36.83 

60.54 

37.10 

60.37 

37.36 

71 

72 

61.72 

37.08 

61.55 

37.35 

61.39 

37.62 

61.23 

37.89 

72 

73 

62.57 

37.60 

62.41 

37.87 

02.24 

38.14 

62.08 

38.41 

73 

74 

63.43 

38.11 

63.26 

38.39 

63.10 

38.66 

62.93 

38.94 

74 

75 

64.29 

38.63 

64.12 

38.91 

63.95 

39.19 

63.78 

39.47 

75 

76 

65.14 

39.14 

64.97 

39.43 

64.80 

39.71 

64.63 

39.99 

76 

77 

66.00 

39.66 

65.83 

39.95 

65.65 

40.23 

65.48 

40.52 

77 

78 

66.86 

40.17 

66.68 

40.46 

66.51 

40.75 

66.33 

41.04 

78 

79 

67.72 

40.69 

67.54 

40.98 

67.36 

41.28 

67.18 

41.57 

79 

80 

68.57 

41.20 

68.39 

41.50 

68.21 

41.80 

68.03 

42.10 

80 

81 

69.43 

41.72 

69.25 

42.02 

69.06 

42.32 

68.88 

42.62 

81 

82 

70.29 

42.23 

70.10 

42.54 

69.92 

42.84 

69.73 

43.15 

82 

83 

71.14 

42.75 

70.96 

43.06 

70.77 

43.37 

70.58 

43.68 

83 

84 

72.00 

43.26 

71.81 

43.58 

71.62 

43.89 

71.43 

44.20 

84 

85 

72.86 

43.78 

72.67 

44.10 

72.47 

44.41 

72.28 

44.73 

85 

86 

73.72 

44.29 

73.52 

44.61 

73.33 

44.93 

73.13 

45.25 

86 

87 

74.57 

44.81 

74.38 

45.13 

74.18 

45.46 

73.98 

45.78 

87 

88 

75.43 

45.32 

75.23 

45.65 

75.03 

45.98 

74.83 

46.31 

88 

89 

76.29 

45.84 

76.09 

46.17 

75.88 

46.50 

75.68 

46.83 

89 

90 

77.15 

46.35 

76.94 

46.69 

76.74 

47.02 

76.53 

47.36 

90 

91 

78.00 

46.87 

77.80 

47.21 

77.59 

47.55 

77.38 

47.89 

91 

92 

78.86 

47.38 

78.65 

47.73 

78.44 

48.07 

78.23 

48.41 

92 

93 

79.72 

47.90 

79.51 

48.25 

79.30 

48.59 

79.08 

48.94 

93 

94 

80.57 

48.41 

80.36 

48.76 

80.15 

49.11 

79.93 

49.47 

94 

95 

81.43 

48.93 

81.22 

49.28 

81.00 

49.64 

80.78 

49.99 

95 

96 

82.29 

49.44 

82.07 

49.80 

81.85 

50.16 

81.63 

50.52 

96 

97 

83.15 

49.96 

82.93 

50.32 

82.71 

50 .68 

82.48 

51.04 

97 

98 

84.00 

50.47 

83.78 

50.84 

83.56 

51.20 

83.33 

51.57 

98 

99 

84.86 

50.99 

84.64 

51.36 

84.41 

51.73 

84.18 

52.10 

99 

100 

85.72 

51.50 

85.49 

51.88 

85.26 

52.25 

85.04 

52.62 

100 

6 

O 

c 

Dep. 


Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

rt 

+-> 

w 

S 

59 Deg. 

58.J Deg. 

58$ 

Deg. 

58$ Deg. 
























































































Oiqtanrf' ^UWMWUUMCSU COMMMMMMMMM »*- h-wmm Mt-wt-}>- 


66 


TRAVERSE TABLE 


o 

CO 

(“► 

p 

3 

o 

o 

• 

• » - — 
1 
2 

3 

4 

K 

o 

6 

7 

8 
9 


32 Deg. 

32i Deg. 

32£ 

Deg. 

32| Deg. 

Distance.! 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

0.85 

0.53 

0.85 

0.53 

0.84 

0.54 

0 84 

0.54 

1 

1.70 

1.06 

1.69 

1.07 

1.69 

1.07 

1.68 

1 08 

2 

2.54 

1.59 

2.54 

1.60 

2.53 

1.61 

2.52 

1.62 

3 

3.39 

2.12 

3.38 

2.13 

3.37 

2.15 

3.36 

2.16 

4 

4.24 

2.65 

4.23 

2.67 

4.22 

2.69 

4.21 

2.70 

5 

5.09 

3.18 

5.07 

3.20 

5.06 

3.22 

5.05 

3.25 

6 

5.94 

3.71 

5.92 

3.74 

5.90 

3.76 

5.80 

3.79 

7 

0.78 

4.24 

6.77 

4.27 

6.75 

4.30 

6.73 

4.33 

8 

7.63 

4.77 

7.61 

4.80 

7.59 

4.84 

7.57 

4.87 

9 

' 8.48 

5.30 

8.46 

5.34 

8.43 

5.37 

8.41 

5.41 

10 

9.33 

5.83 

9.30 

5.87 

9.28 

5.91 

9.25 

5.95 

11 i 

10.18 

6.36 

10.15 

6.40 

10.12 

6.45 

10.09 

6.49 

12 

11.02 

6.89 

10.99 

6.94 

10.96 

6.98 

10.93 

7.03 

13 

11.87 

7.42 

11.84 

7.47 

11.81 

7.52 

11.77 

7.57 

14 

12.72 

7.95 

12.69 

8.00 

12.65 

8.06 

12.62 

8.11 

15 

13.57 

8.48 

13.53 

8.54 

13.49 

8.60 

13.46 

8.66 

16 

14.42 

9.01 

14.33 

9.07 

14.34 

9.13 

14.30 

9.20 

17 

15.23 

9.54 

15.22 

9.61 

15.18 

9.67 

15.14 

9.74 

18 

16.11 

10.07 

16.07 

10.14 

16.02 

10.21 

15.98 

10.28 

19 

16.90 

10.60 

16.91 

10.67 

16.87 

10.75 1 

16.82 

10.82 

20 

17.#1 

11.13 

17.76 

11.21 

17.71 

11.28 

17.66 

11.36 

21 

18.66 

11.66 

18.61 

11.74 

18.55 

11.82 

18.50 

11.90 

22 

19,51 

12.19 

19.45 

12.27 

19.40 

12.36 

19.34 

12.44 

23 

20.35 

12.72 

20.30 

12.81 

20.24 

12.90 : 

20.18 

12.98 

24 

21.20 

13.25 

21.14 

13.34 

21.08 

13.43 

21.03 

13.52 

25 

22.05 

13.78 

21.99 

13.87 

21.93 

13.9.7 | 

21.87 

14.07 

26 

22.90 

14.31 

22.83 

14.41 

22.77 

14.51 

22.71 

14.61 

27 

23.75 

14.84 

23.68 

14.94 

23.61 

15.04 

23.55 

15.15 

28 

24.59 

15.37 

24.53 

15.47 

24.46 

15.58 

24.39 

15.69 

29 

25.44 

15.90 

25.37 

16.01 

25.30 

16.12 ! 

25.23 

16.23 

30 

26.29 

16.43 

26.22 

16.54 

26.15 

16.66 

26.07 

16.77 

31 

27.14 

16.96 

27.06 

17.08 

26.99 

17.19 

26.91 

17.31 

32 

27.99 

17.49 

27.91 

17.61 

27.83 

17.73 

27.75 

17.85 

33 

28.83 

18.02 

28.75 

18.14 

28.68 

18.27 

28.60 

18.39 

34 

29.68 

18.55 

29.60 

18.68 

29.52 

18.81 

29.44 

18.93 

35 

I 30.53 

19.08 

30.45 

19.21 

30.36 

19.34 

30.28 

19.48 

36 

31.38 

19.61 

31.29 

19.74 

31.21 

19.88 

31.12 

20.02 

37 

!32.23 

20.14 

32.14 

20.28 

32.05 

20.42 

31.96 

20.56 

38 

33.07 

20.67 

32.98 

20.81 

32.89 

20.95 

32.80 

21.10 

39 

33.92 

21.20 

33.83 

21.34 

33.74 

21.49 

33.64 

21.64 

40 

34.77 

21.73 

34.67 

21.88 

34.58 

22.03 

34.48 

22.18 

41 

35.62 

22.26 

35.52 

22.41 

35.42 

22.57 

35.32 

22.72 

42 

36.47 

22.79 

36.37 

22.95 

36.27 

23.10 

36.16 

23.26 

43 

37.31 

23.32 

37.21 

23.48 

37.11 

23.64 

37.01 

23.80 

44 

38.16 

23.85 

38.06 

24.01 

37.95 

24.18 

37.85 

24.34 

45 

39.01 

24.38 

38.90 

24.55 

38.80 

24.72 

38.60 

24.88 

46 

39.86 

24.91 

39.75 

25.08 

39.64 

25.25 

39.53 

25.43 

47 

40.71 

25.44 

40.59 

25.61 

40.48 

25.79 

40.37 

25.97 

48 

41.55 

25.97 

41.44 

26.15 

41.33 

26.33 

41.21 

26.51 

49 

42.40 

26.50 

42.29 

26.68 

42.17 

26.86 

42.05 

27.05 

50 

Dep. 

Lai. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<v 

c 

58 Deg. 

1 

57.f Deg. 

57 j Deg. 

57 \ Deg. 

i 

Ctj 

(5 




































































































TRAVERSE TABLE 


67 


D 

E* 

«-► 

p 

32 Deg. 

3*2i Deg. 

32£ Deg. 

32| Deg. 

0 

s* 

3 

n 

CL 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

S3 

O 

a 

• 

61 

43.25 

27.03 

43.13 

27.21 

43.01 

27.40 

42.89 

27.59 

51 

52 

44.10 

27.56 

43.98 

27.75 

43.86 

27.94 

43.73 

28.13 

52 

53 

44,95 

28.09 

44.82 

28.28 

44.70 

28.48 

44.58 

28.67 

53 

54 

45.79 

28.62 

45.67 

28.82 

45.54 

29.01 

45.42 

29.21 

54 

55 

46.64 

29.15 

46.51 

29,35 

46.39 

29.55 

46.26 

29.75 

55 

56 

47.49 

29.68 

47.36 

29.88 

47.23 

30.09 

47.10 

30.29 

56 

57 

48.34 

30.21 

48.21 

30.42 

48.07 

30.63 

47.94 

30.84 

57. 

58 

49.19 

30.74 

49.05 

30.95 

48.92 

31.16 

48.78 

31.38 

58’ 

59 

50.03 

31 27 

49.90 

31.48 

49.76 

31.70 

49.62 

31.92 

59 

60 

50.88 

31.80 

50.74 

32.02 

50.60 

32.24 

50.46 

32.46 

60 

61 

51.73 

32.33 

51.59 

32.55 

51.45 

32.78 

51.30 

33.00 

61 

62 

52.58 

32.85 

52.44 

33.08 

52.29 

33.31 

52.14 

33.54 

62 

63 

53.43 

33.38 

53.28 

33.62 

53.13 

33.85 

52.99 

34.08 

63 

64 

54.28 

33.91 

54.13 

34.15 

53.98 

34.39 

53.83 

34.62 

64 

65 

55.12 

34.44 

54.97 

34.68 

54.82 

34.92 

54.67 

35.16 

65 

66 

55.97 

34.97 

55.82 

35.22 

55.66 

35.46 

55.51 

35.70 

66 

67 

56.82 

35.50 

56.66 

35.75 

56.51 

36.00 

56.35 

36.25 

67 

68 

57.67 

36.03 

57.51 

36.29 

57.35 

36.54 

57.19 

36.79 

68 

69 

58.52 

36.56 

58.36 

36.82 

58.19 

37.07 

58.03 

37.33 

69 

70 

59.36 

37.09 

59.20 

37.35 

59.04 

37.61 

58.87 

37.87 

70 

71 

60.21 

37.62 

60.05 

37.89 

59.88 

38.15 

59.71 

38.41 

71 

72 

61.06 

38.15 

60.89 

38.42 

i60.72 

38.69 

60.55 

38.95 

72 

73 

61.91 

38.68 

61 .74 

38.95 

|61.57 

39.22 

61.40 

39.49 

73 

74 

62.76 

39.21 

62.58 

39.49 

62.41 

39.76 

62.24 

40.03 

74 

75 

63.60 

39.74 

63.43 

40.02 

63.25 

40.30 

!63.08 

40.57 

75 

76 

64.45 

40.27 

64.28 

40.55 

64.10 

40.83 

63.92 

41.11 

76 

77 

65.30 

40.80 

65.12 

41.09 

64.94 

41.37 

64.76 

41.65 

77 

78 

66.15 

41.33 

65.97 

41.62 

65.78 

41.91 

65.60 

42.20 

78 

79 

67.00 

41.86 

66.81 

42.16 

66.63 

42 45 

66.44 

42.74 

79 

80 

67.84 

42.39 

67.66 

42.69 

67.47 

42.98 

67.28 

43.28 

80 

81 

68.69 

42.92 

68.50 

43.22 

68.31 

43.52 

68.12 

43.82 

81 

82 

69.54 

43.45 

69.35 

43.76 

69.16 

44.06 

68.97 

44.36 

82 

S3 

70.39 

43.98 

70.20 

44.29 

70.00 

44.60 

69.81 

44.90 

83 

84 

71.24 

44.51 

71.04 

44.82 

70.84 

45.13 

70.65 

45.44 

84 

85 

72.08 

45.04 

71.89 

45.36 

71.69 

45.67 

71.49 

45.98 

85 

86 

72.93 

45.57 

72.73 

45.89 

72.53 

46.21 

72.33 

46.52 

86 

87 

73.78 

46.10 

73.58 

46.42 

73.38 

46.75 

73.17 

47.06 

87 

88 

74.63 

46.63 

74.42 

46.96 

74.22 

47.28 

74.01 

47.61 

88 

89 

75.48 

47.16 

75.27 

47.49 

75.06 

47.82 

74.85 

48.15 

89 

90 

76.32 

47.69 

76.12 

48.03 

75.91 

48.36 

75.69 

48.69 

90 

91 

77.17 

48.22 

76.96 

48.56 

76.75 

48.89 

76.53 

49.23 

91 

92 

78.02 

48.75 

77.81 

49.09 

77.59 

49.43 

77.38 

49 77 

92 

93 

78.87 

49.28 

78.65 

49.63 

78.44 

49.97 

78.22 

50.31 

93 

91 

79.72 

49.81 

79.50 

50.16 

79.28 

50.51 

79.06 

50.85 

94 

95 

80.56 

50.34 

80.34 

50.69 

80.12 

51.04 

79.90 

51.39 

95 

96 

81.41 

50.87 

81.19 

51.23 

80.97 

51.58 

80.74 

51.93 

96 

97 

82.26 

51.40 

82.04 

51.76 

81.81 

52.12 

81.58 

52.4 7 

97 

98 

83.11 

51.93 

82.88 

52.29 

82.65 

52.66 

82.42 

53.02 

98 

99 

83.96 

52.46 

83.73 

52.83 

83.50 

53.19 

83.26 

53.56 

99 

100 

84.80 

52.99 

81.57 

!53.36 

84.34 

53.73 

84.10 

54.10 

100 

n' 

c: 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.. 

Dep. 

Lat. 

6 

0 

G 

ri 

77 

•H 

58 Deg. 

57| Deg. 

574 Deg. 

57* Deg. 

1 

to 

Q 
































































































G8 TRAVERSE TABLE. 


o 

• 

05 

r*- 

33 Deg. 

33J Deg. 

33i Deg 

33 \ Deg. 

c 

w 

p 

d 

o 

o 

• 

Lat. 

Dep. 

Lat* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

» 

l 

' 1 

0.84 

0.54 

0.84 

0.55 

0.83 

0.55 

0.83 

0.56 

1 

2 

1.68 

1.09 

1.67 

1.10 

1.67 

1.10 

1.60 

1. II 

o 

A 

3 

2.52 

1.63 

2.51 

1.64 

2.50 

1.66 

2.49 

1 67 

3 

4 

3.35 

2.18 

3.35 

2.19 

3.34 

2.21 

3.33 

2.22 

4 

5 

4.19 

2 72 

4.18 

2.74 

4. 17 

2.76 

4.16 

2.78 

5 

0 

5.03 

3 27 

5.02 

3.29 

5.00 

3.31 

4.99 

3.33 

6 

7 

5.87 

381 

5.85 

3.84 

5.84 

3.86 

5.82 

3.89 

7 

8 

6.71 

4.36 

6.69 

4.39 

6.67 

4.42 

6.65 

4.44 

8 

9 

7.55 

4.90 

7.53 

4.93 

7.50 

4.97 

7.48 

5.00 

9 

10 

8.39 

5.45 

8.36 

5.48 

8.34 

5.52 

8.31 

5.56 

10 

11 

9.23 

5.99 

9.20 

6.03 

9.17 

6.07 

9.15 

6.11 

11 

J2 

10.06 

6.54 

10.04 

6.58 

10.01 

6.62 

9.98 

6.67 

12 

13 

10.90 

7.08 

10.87 

7.13 

10.84 

7.18 

10.81 

7.22 

13 

14 

11.74 

7.62 

11.71 

7.68 

11.67 

7.73 

11.64 

7.78 

14 

15 

12.58 

8.17 

12.54 

8.22 

12.51 

8.28 

12.47 

8.33 

15 

16 

13.42 

8.71 

13.38 

8.77 

13.34 

8.83 

13.30 

8.89 

16 

17 

14.26 

9.26 

14.22 

9.32 

14.18 

9.38 

14.13 

9.44 

17 

18 

15.10 

9.80 

15.05 

9.87 

15.01 

9.93 

14.97 

10.00 

18 

19 

15.93 

10.35 

15.89 

10.42 

15.84 

10.49 

15.80 

10.56 

19 

20 

16.77 

10.89 

16.73 

10.97 

16.68 

11.04 

16.63 

11.11 

20 

21 

17.61 

11.44 

17.56 

11.51 

17.51 

11.59 

17.46 

11.67 

21 

22 

18.45 

11.98 

18.40 

12.06 

18.35 

12.14 

18.29 

12.22 

22 

23 

19.29 

12.53 

19.23 

12.61 

19.18 

12.69 

19.12 

12.78 

23 

24 

20.13 

13.07 

20.07 

13.16 

20.01 

13.25 

19.96 

13.33 

24 

25 

20.97 

13.62 

20.91 

13.71 

20.85 

13.80 

20.79 

13.89 

25 

26 

21.81 

14.16 

21.74 

14.26 

21.68 

14.35 

21.62 

14.44 

26 

27 

22.64 

14.71 

22.58 

14.80 

22.51 

14.90 

22.45 

15.00 

27 

28 

23.48 

15.25 

23.42 

15.35 

23.35 

15.45 

23.28 

15.56 

28 

29 

24.32 

15.79 

24.25 

15.90 

24.18 

16.01 

24.11 

16.11 

29 

30 

25.16 

16.34 

25.09 

16.45 

25.02 

16.56 

24.94 

16.67 

30 

31 

26.00 

16.88 

25.92 

17.00 

25.85 

17.11 

25.78 

17.22 

31 

32 

26.84 

17.43 

26.76 

17.55 

26.68 

17.66 

26.61 

17.78 

32 

33 

27.68 

17.97 

27.60 

18.09 

27.52 

18.21 

27.44 

18.33 

33 

34 

28.51 

18.52 

28.43 

18.64 

28.35 

18.77 

28.27 

18.S9 

34 

35 

29.35 

19.06 

29.27 

19.19 

29.19 

19.32 

29.10 

19.44 

35 

36 

30.19 

19.61 

30.11 

19.74 

30.02 

19.87 

29.93 

20.00 

36 

37 

31.03 

20.15 

30.94 

20.29 

30.85 

20.42 

30.76 

20.56 

37 

38 

31.87 

20.70 

31.78 

20.84 

31.69 

20.97 

31.60 

21.11 

38 

39 

32.71 

21.24 

32.62 

21.38 

32.52 

21.53 

|32.43 

21.67 

39 

40 

33.55 

21.79 

33.45 

21.93 

33.36 

22.08 

33.26 

22.22 

40 

41 

34.39 

22.33 

34.29 

22.48 

34.19 

22.63 

34.09 

22.78 

41 

42 

35.22 

22.87 

35.12 

23.03 

35.02 

23.18 

34.92 

23.33 

42 

43 

36.06 

23.42 

35.96 

23.58 

35.86 

23.73 

35.75 

23.89 

43 

44 

36.90 

23.96 

36.80 

24.12 

36.69 

24.29 

36.58 

24.45 

44 

45 

37.74 

24.51 

37.63 

24.67 

37.52 

24.84 

37.42 

25 00 

45 

46 

38.58 

25.05 

38.47 

25.22 

3S.36 

25.39 

38.25 

25.56 

46 

47 

39.42 

25.60 

39.31 

25.77 

39.19 

25.94 

39.08 

26.11 

47 * 

48 

40.26 

26.14 

40.14 

26.32 

40.03 

26.49 

39.91 

26.67 

48 

49 

41.09 

26.69 

40.98 

26.87 

40.86 

27.04 

40.74 

27.22 

49 

50 

41.93 

27.23 

41.81 

27.41 

41.69 

27.60 

41.57 

27.78 

50 

d 

o 

a 

Dep. 

Lat. 

Dep. 

Lat* 

Dep. 

Lat. 

Dep. 

Lat* 

ai 
o 
t c 

00 

10 
• *-* 

Q 

57 Deg. 

56f Deg. 

56 i Deg. 

56 J Deg. 

C0 

T© 

• *■* 

Q 







































































































TRAVERSE TABLE 


69 


o 

►-» 

oo 

H 

P 

33 Deg. 


33i 

Deg. 


33^ 

Deg. 


331 

Deg. 

' 1 ?! 

a 
►— • 

X 

pr 

o 

CD 

Lat. 

Dep. 

Lat. 

Dop. 

Lat. 

Dep. 

Lat. 

Dep. 

b 

o 

CD 

51 

42 

.77 

27. 

78 

42 

.65 

27.96 

42 

.53 

28.15 

42 

.40 

28. 

33 

51 

52 

43 

.61 

28. 

32 

43 

.49 

28.51 

43 

.36 

28.70 

43 

.24 

28. 

89 

52 

53 

44 

.45 

28. 

87 

44 

.32 

29.06 

44 

.20 

29.25 

44 

.07 

29 

45 

53 

54 

45 

.29 

29. 

41 

45 

.16 

29.61 

45 

.03 

29.80 

44 

.90 

30. 

00 

54 

55 

46 

.13 

29. 

96 

46 

.00 

30.16 

45 

.86 

30.36 

45 

.73 

30. 

56 

55 

66 

46 

.97 

30. 

50 

46 

.83 

30.70 

46 

.70 

30.91 

46 

.56 

31 

11 

56 

67 

47 

.80 

31. 

04 

47 

.67 

31.25 

47 

.53 

31.46 

47 

.39 

31 

67 

57 

58 

48 

. 64 

31. 

59 

48 

.50 

31.80 

48 

.37 

32.01 

48 

.23 

32. 

22 

58 

59 

49 

.48 

32. 

13 

49 

.34 

32.35 

49 

.20 

32.56 ! 

49 

.06 

32. 

78 

59 

60 

50 

.32 

32. 

68 

50 

.18 

32.90 

50 

.03 

33.12 

49 

.89 

33. 

33 

60 

61 

51 

.16 

33. 

22 

51 

.01 

33.45 

50 

.87 

33.67 

50 

.72 

33. 

89 

61 

62 

52 

.00 

33. 

77 

51 

.85 

33.99 

51 

.70 

34.22 

51 

.55 

34. 

45 

62 

63 

52 

.84 

34. 

31 

52 

.69 

34.54 

52 

.53 

34.77 

52 

.38 

35. 

00 

63 

64 

53 

.67 

34. 

86 

53 

.52 

35.09 

53 

.37 

35.32 

53 

.21 

35. 

56 

64 

65 

54 

.51 

35. 

40 

54 

.36 

35.64 

54 

.20 

35.88 

54 

05 

36. 

11 

65 

66 

55 

.35 

35. 

95 

55 

.19 

36.19 

55 

.04 

36.43 

54 

.88 

36. 

67 

pj 

67 

56 

.19 

36. 

49 

56 

.03 

36.74 

55 

.87 

36.98 

55 

.71 

37. 

22 

'67 

68 

57 

.03 

37. 

04 

56 

.87 

37.28 

56 

.70 

37.53 

56 

.54 

37. 

78 

68 

69 

57 

.87 

37. 

58 

57 

.70 

37.83 

57 

.54 

38.08 

57 

.37 

38. 

33 

69 

70 

58 

.71 

38. 

12 

58 

.54 

38.38 

58 

.37 

38.64 

58 

.20 

38. 

89 

70 

71 

59 

.55 

38. 

67 

59 

.38 

38.93 

59 

.21 

39.19 

59 

.03 

39. 

45 

71 

72 

60 

.38 

39. 

21 

60 

.21 

39.48 

60 

.04 

39.74 

59 

.87 

40. 

00 

72 

73 

61 

.22 

39. 

76 

61 

.05 

40.03 

60 

.87 

40.29 

60 

.70 

40. 

56 

73 

74 

62 

.06 

40. 

30 

61 

.89 

40.57 

61 

.71 

40.84 

61 

.53 

41. 

11 

74 

75 

62 

.90 

40. 

85 

62 

.72 

41.12 

62 

.54 

41.40 

62 

.36 

41. 

67 

75 

76 

63 

.74 

41. 

39 

63 

.56 

41.67 

63 

.38 

41.95 

63 

19 

42. 

22 

76 

77 

64 

.58 

41. 

94 

64 

.39 

42.22 

64 

.21 

42.50 

64 

.02 

42. 

78 

77 

78 

65 

.42 

42. 

48 

65 

.23 

42.77 

65 

.04 

43.05 

64 

.85 

43. 

33 

78 

79 

06 

.25 

43. 

03 

66 

.07 

43.32 

65 

.88 

43.60 

65 

.69 

43. 

89 

79 

80 

67 

.09 

43. 

57 

66 

.90 

43.86 

66 

.71 

44.15 

66 

.52 

44. 

45 

80 

81 

67 

.93 

44. 

12 

67 

.74 

44.41 

67 

.54 

44.71 

67 

.35 

45. 

00 

81 

82 

68 

.77 

44. 

66 

68 

.58 

44.96 

68 

.38 

45.26 

68 

.18 

45. 

56 

82 

83 

69 

.61 

45. 

20 

69 

.41 

45.51 

69 

.21 

45.81 

69 

.01 

46. 

11 

83 

84 

70 

.45 

45. 

75 

70 

.25 

46.06 

70 

.05 

46.36 

69 

.84 

46. 

67 

84 

85 

71 

.29 

46. 

29 

71 

.08 

46.60 

70 

.88 

46.91 

70 

.67 

47. 

22 

85 

86 

72 

.13 

46. 

84 

71 

.92 

47.15 

71 

.71 

47.47 

71 

.51 

47. 

78 

86 

87 

72 

.96 

47. 

38 

72 

.76 

47.70 

72 

.55 

48.02 

72 

.34 

48. 

33 

87 

88 

73 

.80 

47. 

93 

73 

.59 

48.25 

73 

.38 

48.57 

73 

.17 

48. 

89 

88 

89 

74 

.64 

48. 

47 

74 

.43 

48.80 

74 

.22 

49.12 

74 

.00 

49. 

45 

89 

90 

75 

.48 

49. 

02 

75 

.27 

49.35 

75 

.05 

49.67 

! 74 

.83 

50 

00 

90 

91 

76 

.32 

49. 

56 

76 

.10 

49.89 

75 

.88 

50.23 

75 

. 66 

50 

56 

91 

92 

77 

.16 

50. 

11 

76 

.94 

50.44 

76 

.72 

50.78 

1 76 

.50 

51 

.11 

92 

93 

78 

.00 

50. 

65 

77 

.77 

50.99 

77 

.55 

51.33 

77 

.33 

51 

.67 

93 

94 

78 

.83 

51. 

20 

78 

.61 

51.54 

78 

.39 

51.88 

78 

.16 

52 

.22 

94 

95 

79 

.67 

51. 

74 

79 

.45 

52.09 

79 

.22 

52.43 

78 

.99 

52 

.78 

95 

96 

80 

.51 

52. 

29 

80 

.28 

52.64 

80 

.05 

52.99 

79 

.82 

53 

.33 

96 

97 

81 

.35 

52. 

83 

81 

.12 

53.18 

80 

.89 

53.54 

1 80 

.65 

53 

.89 

| 97 

98 

82 

.19 

53. 

37 

81 

.96 

53.73 

81 

.72 

54.09 

81 

.48 

54 

.45 

' 98 

99 

83 

.03 

53. 

92 

82 

.79 

54.28 

82 

.55 

54.64 

82 

.32 

55 

.00 

99 

100 

83 

.87 

54. 

46 

83 

.63 

54.83 

83 

.39 

55.19 

83 

.15 

55 

. 56 

i 00 

o 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

L 

at. 

o 

w 

cd 

4-» 

Ifl 

• *4 

a 

57 Deg. 


56? 

Dog. 


56‘- 

Deg. 

1 

| 

66} 

Deg. 

rt 

/■■s 

i 









































































































0 


TRAVERSE TABLE 


1 — 

e 

►— 

CD 

34 Deg. 

34$ Deg. 

-|(M 

3 

Deg. 

34| Deg. 

O 

• 

73 

*"♦ 

P 

3 

a 

a 

Lat. 

Dep. 

Ldt* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

§ 

T 

0.83 

0.56 

0.83 

0.56 

0.82 

0.57 

0. 82 

C .57 

1 

2 

1.66 

1.12 

1.65 

1.13 

1.65 

1.13 

1.64 

1.14 

O 

3 

2.49 

1.68 

2.48 

1.69 

2.47 

1.70 

2.46 

1.71 

3/ 

4 

3.32 

2.24 

3.31 

2.25 

3.30 

2.27 

3.29 

2.28 

4 

5 

4.15 

2.80 

4.13 

2.81 

4.12 

2.83 

4.11 

2.85 

q 

6 

4.97 

3.36 

4.96 

3.38 

4.94 

3.441 

4.93 

3.42 

f, \ 

7 

5.80 

3.91 

5.79 

3.94 

5.77 

3.96 

5.75 

3.99 


8 

6.63 

4.47 

6.61 

4.50 

6.59 

4.53 

6.57 

4.56 

9 

9 

7.46 

5.03 

7.44 

5.07 

7.42 

5.10 

7.39 

5.13 

9 

10 

8.29 

5.59 

8.27 

5.63 

8.24 

5.66 

8.22 

5.70 

to 

11 

9.12 

6.15 

9.09 

6.19 

9.07 

6.23 

9.04 

6.27 

11 

12 

9.95 

6.71 

9.92 

6.75 

9.89 

6.80 

9.86 

6.84 

12 

13 

10.78 

7.27 

10.75 

7.32 

10.71 

7.36 

10.68 

7.41 

13 

14 

11.61 

7.83 

11.57 

7.88 

11.54 

7.93 

11.50 

7.98 

14 

15 

12.44 

8.39 

12.40 

8.44 

12.36 

8.50 

12.32 

8.55 

15 

16 

13.26 

8.95 

13.23 

9.00 

13.19 

9.06 

13.15 

9.12 

16 

17 

14.09 

9.51 

14.05 

9.57 

14.01 

9.63 

13.97 

9.69 

17 

18 

14.92 

10.07 

14.88 

10.13 

14.83 

10.20 

14.79 

10.26 

18 

19 

15.75 

10.62 

15.71 

10.69 

15.66 

10.76 

15.61 

10.83 

19 

20 

16.58 

11.18 

16.53 

11.26 

16.48 

11.33 

16.43 

11.40 

20 

21 

17.41 

11.74 

17.36 

11.82 

17.31 

11.89 

17.25 

11.97 

21 

22 

18.24 

12.30 

18.18 

12.38 

18.13 

12.46 

18.08 

12.54 

22 

23 

19.07 

12.86 

19.01 

12.94 

18.95 

13.03 

18.90 

13.1! 

23 

24 

19.90 

13.42 

19.84 

13.51 

19.78 

13.59 

19.72 

13.68 

24 

25 

20.73 

13.98 

20.66 

14.07 

20.60 

14.16 

20.54 

14.25 

25 

26 

21.55 

14.54 

21.49 

14.63 

21.43 

14.73 

21.36 

14.82 

26 

27 

22.38 

15.10 

22.32 

15.20 

22.25 

15.29 

22.18 

15.39 

27 

28 

23.21 

15 66 

23.14 

15.76 

23.08 

15.86 

23.01 

15.96 

28 

29 

24.04 

16.22 

23.97 

16.32 

23.90 

16.43 

23.83 

16.53 

29 

30 

24.87 

16.78 

24.80 

16.88 

24.72 

16.99 

24.65 

17.10 

30 

31 

25.70 

17.33 

25. G2 

17.45 

25.55 

17.56 

25.47 

17.67 

31 

32 

26.53 

17.89 

26.45 

18.01 

26.37 

18.12 

26.29 

18.24 

32 

33 

27.36 

18.45 

27.28 

18.57 

27.20 

18.69 

27.11 

18.81 

33 

34 

28.19 

19.01 

28.10 

19.14 

28.02 

19.26 

27.94 

19.38 

34 

35 

29.02 

19.57 

28.93 

19.70 

28.84 

19.82 

28.76 

19.95 

35 

36 

29.85 

20.13 

29.76 

20.26 

29.67 

20.39 

29.58 

20.52 

36 

37 

30.67 

20.69 

30.58 

20.82 

30.49 

20.96 

30.40 

21.09 

.r 

38 

31.50 

21.25 

31.41 

21.39 

31.32 

21.52 

31.22 

21.66 

38 

39 

32.33 

21.81 

32.24 

21.95 

32.14 

22.09 

32.04 

22.23 

39 

40 

33.16 

22.37 

33.06 

22.51 

32.97 

22.66 

32.87 

22.80 

40 

41 

33.99 

22.93 

33.89 

23.07 

33.79 

23.22 

33.69 

23.37 

4 l 

42 

34.82 

23.49 

34.72 

23 64 

34.61 

23.79 

34.51 

23.94 

42 

43 

35.65 

24.05 

35.54 

24 20 

35.44 

24.36 

35.33 

24.51 

43 

44 

36.48 

24.60 

36.37 

24 76 

36.26 

24.92 

36.15 

25.08 

44 

15 

37.31 

25.16 

37.20 

25 33 

37.09 

25.49 

36.97 

25.65 

45 

46 

1 38.14 

25.72 

38.02 

25 89 

37.91 

26.05 

37.80 

26.22 

46 

47 

38.96 

26.28 

38.85 

26.45 

38.73 

26.62 

38.62 

26.79 

47 

48 

39.79 

26.84 

39.68 

27.01 

39.56 

27.19 

39.44 

27.36 

48 

49 

40.62 

27.40 

40.50 

27.58 

40.38 

27.75 

40.26 

27.93 

49 

50 

41.45 

27.96 

41.33 

28.14 

41.21 

28.32 

41.08 

28.50 

50 

© 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

V 

c 

cd 

«-> 

ID 

Q 

56 Deg. 

I 

551 Deg. 

55i 

Deg. 

5h\ Deg. 

eri 

W3 

5 






































































































TRAVERSE table 


71 


o 

5 

r* 

P 

34 Deg. 

34$ Deg. 

341 

Deg. 

34$ Deg. 

O 

5* 

p 

3 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

CD 

a 

61 

42.28 

28.52 

42.16 

28.70 

42.03 

28.89 

41.90 

29.07 

51 

62 

43.11 

29.08 

42.98 

29.27 

42.85 

29.45 

42.73 

29.64 

52 

63 

43.94 

29.64 

43.81 

29.83 

43.68 

30.02 

43.55 

30.21 

53 

54 

44.77 

30.20 

44.64 

30.39 

44.50 

30.59 

44.37 

30 78 

54 

55 

45.60 

30.76 

45.46 

30.95 

45.33 

31.15 

45.19 

31.35 

55 

56 

46.43 

31.31 

46.29 

31 .52 

46.15 

31.72 

46 01 

31.92 

56 

57 

47.26 

31.87 

47.12 

32.08 

46.98 

32 29 

46.83 

32.49 

57 

58 

48.08 

32.43 

47.94 

32.64 

47.80 

32.85 

47.66 

33.06 

58 

59 

48.91 

32.99 

48.77 

33.21 

48.62 

33.42 

48.48 

33.63 

59 

60 

49.74 

33.55 

49.60 

33.77 

49.45 

33.98 

49.30 

34.20 

60 

61 

50.57 

34.11 

50.42 

34.33 

50.27 

34.55 

50.12 

34.77 

61 

62 

51.40 

34.67 

51.25 

34.89 

51.10 

35.12 

50.94 

35.34 

62 

63 

52.23 

35.23 

52.08 

35.46 

51.92 

35.68 

51.76 

35.91 

63 

64 

63.06 

35.79 

52.90 

36.02 

52.74 

36.25 

52.59 

36.48 

64 

65 

53.89 

36.35 

53.73 

36.58 

53.57 

36.82 

53.41 

37.05 

65 

66 

54.72 

36.91 

54.55 

37.15 

54.39 

37.38 

54.23 

37.62 

66 

67 

55.55 

37.46 

55.38 

37.71 

55.22 

37.95 

55.05 

3 S . 19 

67 

68 

56.37 

38.03 

56.21 

38.27 

56.04 

38.52 

55.87 

38.76 

68 

69 

57.20 

38.58 

57.03 

38.83 

56.86 

39.08 

56.69 

39.33 

69 

70 

58.03 

39.14 

57.86 

39.40 

57.69 

39.65 

57.52 

39.90 

70 

71 

58.86 

39.70 

58.69 

39.96 

58.51 

40.21 

58.34 

40.47 

71 

72 

59.69 

40.26 

59.51 

40.52 

59.34 

40.78 

59.16 

41.04 

72 

73 

60.52 

40.82 

60.34 

41.08 

60.16 

41.35 

59.98 

41.61 

73 

74 

61.35 

41.38 

61.17 

41.65 

60.99 

41.91 

60.80 

42.18 

74 

75 

62.18 

41.94 

61.99 

42.21 

61.81 

42.48 

61.62 

42.75 

75 

76 

63.01 

42.50 

62.82 

42.77 

62.63 

43.05 

62.45 

43.32 

76 

77 

63.84 

43.06 

63.65 

43.34 

63.46 

43.61 

63.27 

43.89 

77 

78 

64.66 

43.62 

64.47 

43.90 

64.28 

44.18 

64.09 

44.46 

78 

79 

65.49 

44.18 

65.30 

44.46 

65.11 

44.75 

64.91 

45.03 

79 

80 

66.32 

44.74 

66.13 

45.02 

65.93 

45.31 

65.73 

45.60 

80 

81 

67.15 

45.29 

66.95 

45.59 

66.75 

45.88 

66.55 

46.17 

81 

82 

67.98 

45.85 

67.78 

46.15 

67.58 

46.45 

67.37 

46.74 

82 

83 

68.81 

46.11 

68.61 

46.71 

68.40 

47.01 

68.20 

47.31 

83 

84 

69.64 

46.97 

69.43 

47.28 

69.23 

47.58 

69.02 

47.88 

84 

85 

70.47 

47.53 

70.26 

47.84 

70.05 

48.14 

69.84 

48.45 

85 

86 

71.30 

48.09 

71.09 

48.40 

70.87 

48.71 

70.66 

49.02 

86 

87 

72.13 

48.65 

71.91 

48.96 

71.70 

49.28 

71.48 

49.59 

87 

88 

72.96 

49.21 

72.74 

49.53 

72.52 

49.84 

72.30 

50.16 

88 

89 

73.78 

49.77 

73.57 

50.09 

73.35 

50.41 

73.13 

50 73 

89 

90 

74.61 

50.33 

74.39 

50.65 

74.17 

50.98 

73.95 

51.30 

90 

91 

75.44 

50.89 

75.22 

51.22 

75.00 

51.54 

74.77 

51.87 

91 

92 

76.27 

51.45 

76.05 

51.78 

75.82 

52.11 

75.59 

52.44 

92 

93 

77.10 

52.00 

76.87 

52.34 

76.64 

52.68 

76.41 

53.01 

93 

94 

77.93 

52.56 

77.70 

52.90 

77.47 

53.24 

77.23 

53.58 

94 

95 

78.76 

53.12 

78.53 

53.47 

78.29 

53.81 

78.06 

54. 15 

95 

96 

79.59 

53.68 

79.35 

54.03 

79.12 

54.37 

78.88 

54.72 

96 

97 

80.42 

54.24 

80. IS 

54.59 

79.94 

54.94 

79 70 

55.29 

97 

98 

81.25 

54.80 

81.01 

55.15 

80.76 

55.51 

80 52 

55.86 

98 

99 

82.07 

55.36 

81.83 

55.72 

81.59 

56.07 

81.34 

56.43 

99 

100 

82.90 

55.92 

82.66 

56.28 

82.41 

56.64 

82.16 

57.00 

100 

03 

O 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<u 

V 

G 

rd 

«•-> 

OQ 

• 

a 

58 Deg. 

55| Deg. 

55 j 

Deg. 

55$ Deg. 

«-» 

c n 

1 ^ 















































































72 


TRAVERSE TABLE 


d 

to 

r* 

35 Deg. 

35} Deg. 

35} Deg. 

35} Deg. 

O 

5T 

p0 

3 

3 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

1 ? 

1 

0.82 

0.57 

0.82 

0.58 

0.81 

0.58 

0.81 

0.58 

1 

o 

-V 

1.64 

1.15 

1.63 

1.15 

1.63 

1.16 

1.62 

1.17 

2 

3 

2.46 

1.72 

2.45 

1.73 

2.44 

1.74 

2.43 

1.75 

' 3 

1 

3.28 

O OQ 

A* • 

3.27 

2.31 

3.26 

2.32 

3.25 

2.31 

4 

5 

4.10 

2.87 

4.08 

2.89 

4.07 

2.90 

1.06 

2.92 

5 

6 

4.91 

3.44 

4.90 

3.46 

4.88 

3.48 

4.87 

3.511 6 

7 

5.73 

4.01 

5.72 

4.04 

5.70 

4.06 

5.68 

4.09 

7 

8 

6.55 

4.59 

6.53 

4.62 

6.51 

4.65 

6.49 

4.67 

8 

9 

7.37 

5.16 

7.35 

5.19 , 

7.33 

5.23 

7.30 

5.26 

9 

10 

8.19 

5.74 

8.17 

5.77 

8.14 

5.81 

8.12 

5.84 

to 

11 

9.01 

6.31 

8.98 

6.35 

8.96 

6.39 

8.93 

6.43 

11 

12 

9.83 

6.88 

9.80 

6.93 

9.77 

6.97 

9.74 

7.01 

12 

13 

10.65 

7.46 

10.62 

7.50 

10.58 

7.55 

10.55 

7.60 

13 

11 

11.47 

8.03 

11.43 

8.08 

11.40 

8.13 

11.36 

8.18 

14 

15 

12.29 

8.60 

12.25 

8.66 

12.21 

8.71 

12.17 

8.76 

15 

16 

13.11 

9.18 

13.07 

9.23 

13.03 

9.29 

12.99 

9.35 

16 

17 

13.93 

9.75 

13.88 

9.81 

13.84 

9.87 

13.80 

9.93 

17 

IS 

14.74 

10.32 

14.70 

10.39 

14.65 

10.45 

14.61 

10.52 

18 

19 

15.56 

10.90 

15.52 

10.97 

15.47 

11.03 

15.42 

11.10 

19 

20 

16.38 

11.47 

16.33 

11.54 

16.28 

11.61 

16.23 

11.68 

20 

21 

17.20 

12.05 

17.15 

12.12 

17.10 

12.19 

17.04 

12.27 

21 

22 

18.02 

12.62 

17.97 

12.70 

17.91 

12.78 

17.85 

12.85 

22 

23 

18.84 

13.19 

18.78 

13.27 

18.72 

13.36 

18.67 

13.44 

23 

24 

19.66 

13.77 

19.60 

13.85 

19.54 

13.94 

19.48 

14.02 

24 

25 

20.48 

14.34 

20.42 

14.43 

20.35 

14.52 

20.29 

14.61 

25 

26 

21.30 

14.91 

21.23 

15.0' 

21.17 

15.10 

21.10 

15.19 

26 

27 

22.12 

15.49 

22.05 

15.58 

21.98 

15.68 

21.91 

15.77 

27 

28 

22.94 

16.06 

22.87 

16.13 

22.80 

16.26 | 

22.72 

16.36 

28 

29 

23.76 

16.63 

23.68 

16.74 

23.61 

16.84 

23.54 

16.94 

29 

30 

24.57 

17.21 

24.50 

17.51 

24.42 

17.42 

24.35 

17.53 

30 

31 

25.39 

17.78 

25.32 

17.89 

25.24 

18.00 

25.16 

18.11 

31 

32 

26.21 

18.35 

26.13 

18.47 

26.05 

18.58 

25.97 

18.70 

32 

33 

27.03 

18.93 

26.95 

19.05 

26.87 

19.16 

26.78 

19.28 

33 

34 

27.85 

19.50 

27.77 

19.62 

27.68 

19.74 

27.59 

19.86 

34 

35 

23.67 

20.08 

28.58 

20.20 

28.49 

20.32 

28.41 

20.45 

35 

36 

29.49 

20.65 

29.40 

20.78 

29.31 

20.91 

29.22 

21.03 

36 

37 

30.31 

21.22 

30.22 

21.35 

30.12 

21.49 

130.03 

21.62 

37 

38 

31.13 

21.80 

31.03 

21.93 

30.94 

22.07 

30.84 

22.20 

38 

39 

31.95 

22.37 

31.85 

22.51 

31.75 

22.65 

31.65 

22.79 

39 

40 

32.77 

22.94 

32.67 

23.09 

32.56 

23.23 

|32.46 

23.37 

40 

41 

33.59 

23.52 

33.48 

23.66 

33.38 

23.81 

133.27 

23.95 

41 

42 

34.40 

24.09 

34.30 

24.24 

34.19 

24.39 

34.09 

24.54 

42 

43 

35.22 

24.66 

35.12 

24.82 

35.01 

21.97 

134.90 

25.12 

43 

44 

36.04 

25.24 

35.93 

25.39 

35.82 

25.55 

35.71 

25.71 

44 

45 

36.86 

25.81 

36.75 

25.97 

36.64 

26.13 

i 36.52 

26.29 

45 

46 

37.68 

26.38 

37.57 

26.55 

37.45 

26.71 

j 37.33 

26,88 

46 

47 

38.50 

26.96 

38.38 

27.13 

38.26 

27.29 

138.14 

27.46 

47 

48 

39.32 

27.53 

39.20 

27.70 

39.08 

27.87 

i 38.96 

28.04 

48 

49 

40. 14 

28.11 

40.02 

28.28 

39.89 

28.45 

39.77 

28.63 

49 

50 

40.96 

28.68 

40.83 

28.86 

40.71 

29.04 

40.58 

29.21 

50 

aS 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

ai 

o 

c 

ci 

5 

55 Deg. 

54} Deg. 

54} Deg. 

54} Deg : 

cd 

«♦-» 

CO 

• H 

a 


























































































TKAVEKSE TABLE. 


73 


Distance.| 

35 Deg. 

35 i Deg. 

35 £ Deg. 

351 Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

41,78 

29.25 

41.65 

29.43 

41.52 

29.62 

41.39 

29.80 

51 

52 

42.60 

29.82 

42.47 

30.01 

42.33 

30.20 

42.20 

30.38 

52} 

53 

43.42 

30.40 

43.28 

30.59 

43.15 

30.78 

43.01 

30.97 

53/ 

54 

44.22 

30.97 

44.10 

31.17 

43.96 

31.36 

43.82 

3 J .55 

54 [ 

55 

45.05 

31.55 

44.92 

31.74 

44.78 

31.94 

44.64 

32.13 

551 

56 

45.87 

32.12 

45.73 

32.32 

45.59 

32.52 

45.45 

32.72 

56 

57 

46.69 

32.69 

46.55 

32.90 

46.40 

33.10 

46.26 

33.30 

57 

58 

47.51 

33.27 

47.37 

33.47 

47.22 

33.68 

47.07 

33.89 

58 | 

59 

48.33 

33.84 

48.18 

34.05 

48.03 

34.26 

47.88 

34.47 

59 

60 

49.15 

34.41 

49.00 

34.63 

48.85 

34.84 

48.69 

35.05 

60 

61 

49.97 

34.99 

49.82 

35.21 

49.66 

35.42 

49.51 

35.64 

61 

62 

50.79 

35.56 

50.63 

35.78 

50.48 

36.00 

50.32 

36.22 

62 

63 

51.61 

36.14 

51.45 

36.36 

51.29 

36.58 

51.13 

36.81 

63 

64 

52.43 

36.71 

52.27 

36.94 

52.10 

37.16 

51.94 

37.39 

64 

65 

53.24 

37.28 

53.08 

37.51 

52.92 

37.75 

52.75 

37.98 

65 

66 

54.06 

37.86 

53.90 

38.09 

53.73 

38.33 

63.56 

38.56 

66 

67 

54.88 

38.43 

54.71 

38.67 

54.55 

38.91 

54.38 

39.14 

67 

68 

55.70 

39.00 

55.53 

39.25 

55.36 

39.49 

55.19 

39.73 

68 

69 

56.52 

39.58 

56.35 

39.82 

56.17 

40.07 

56.00 

40.31 

69 

70 

57.34 

40.15 

57.16 

40 40 

56.99 

40.65 

56.81 

40.90 

70 

71 

58.16 

40.72 

57.98 

40.98 

57.80 

41.23 

57.62 

41.48 

71 

72 

58.98 

41.30 

58.80 

41.55 

58.62 

41.81 

58.43 

42.07 

72 

73 

59.80 

41.87 

59.61 

42.13 

59.43 

42.39 

59.24 

42.65 

73 

74 

60.62 

42.44 

60.43 

42.71 

60.24 

42.97 

60.06 

43.23 

74 

75 

61.44 

43.02 

61.25 

43.29 

61.06 

43.55 

60.87 

43.82 

75 

76 

62.26 

43.59 

62.06 

43.86 

61.87 

44.13 

61.68 

44.40 

76 

77 

63.07 

44.17 

62.88 

44.44 

62.69 

44.71 

62.49 

44.99 

77 

78 

63.89 

44.74 

63.70 

45.02 

63.50 

45.29 

63.30 

45.57 

78 

79 

64.71 

45.31 

64.51 

45.59 

64.32 

45.88 

64.11 

46.16 

79 

80 

65.53 

45.89 

65.33 

46.17 

65.13 

46.46 

64.93 

46.74 

80 

81 

66.35 

46.46 

66.15 

46.75 

65.94 

47.04 

65.74 

47.32 

81 

82 

67.17 

47.03 

66.90 

47.33 

66.76 

47.62 

66.55 

47.91 

82 

83 

67.99 

47.61 

67.78 

47.90 

67.57 

48.20 

67.36 

48.49 

83 

84 

68.81 

48.18 

68.60 

48.48 

68.39 

48.78 

68.17 

49.08 

84 

85 

69.63 

48.75 

69.41 

49.06 

69.20 

49.36 

68.98 

49.66 

85 

86 

70.45 

49.33 

70.23 

49.63 

70.01 

49.94 

69.80 

50.25 

86 

87 

71.27 

49.90 

71.05 

50.21 

70.83 

50.52 

70.61 

50.83 

87 

88 

72.09 

50.47 

71.86 

50.79 

71.64 

51.10 

71.42 

51.41 

88 

89 

72.90 

51.05 

72.68 

51.37 

72.46 

51.68 

72.23 

52.00 

89 

90 

73.72 

51.62 

73.50 

51.94 

73.27 

52.26 

73.04 

52.58 

90 

91 

74.54 

52.20 

74.31 

52.52 

74.08 

52.84 

73.85 

53.17 

91 

92 

75.36 

52.77 

75.13 

53.10 

74.90 

53.42 

74.66 

53.75 

92 

93 

76.18 

53.34 

75.95 

53.67 

75.71 

54.01 

75.48 

54.34 

93 

94 

77.00 

53.92 

76.76 

54.25 

76.53 

54.59 

76.29 

54.92 

94 

95 

77.82 

54.49 

77.58 

54.83 

77.34 

55.17 

77 10 

55.50 

95 

96 

78.64 

55.06 

78.40 

55.41 

78.16 

55.75 

77.91 

56.09 

96 

97 

79.46 

55.64 

79.21 

55.98 

78 97 

56.33 

78.72 

56.67 

97 

98 

80.28 

56.21 

80.03 

56.56 

79.78 

56.91 

79.53 

57.26 

98 

99 

81.10 

56.78 

80.85 

57.14 

80.60 

57.49 

80.35 

57.84 

99 

100 

81.92 

57.36 

81.66 

57.71 

81.41 

58.07 

81.16 

5 8.42 

100 

© 

o 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

c 

Ct 

Cfi 

p 

55 Deg. 

54$ Deg. 

54i Deg. 

54$ Deg. 

f 

oi 

V. 

a 








































































































74 


TRAVERSE TABLE 


o 

S' 

r** 

36 D eg. 

36} Deg. 

36£ 

Deg. 

36} Deg. 

O 

00 

r-* 

P 

3 

n 

ffl 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

0 

a 

• 

i 

0.81 

0.59 

0.81 

0.59 

0.80 

0.59 

0.80 

0.60 

1 

2 

1.62 

1.18 

1.61 

1.18 

1.61 

1.19 

1.60 

1 20 

2 

3 

2.43 

1.76 

2.42 

1.77 

2.41 

1.78 

2.40 

1.79 

3 

4 

3.24 

2.35 

3.23 

2.37 

3.22 

2.38 

3.20 

2.39 

4 

5 

4.05 

2.94 

4.03 

2.96 

4.02 

2.97 

4.01 

2.99 

5 

6 

4.85 

3.53 

4.84 

3.55 

4.82 

3.57 

4.81 

3.59 

6 

7 

5.66 

4.11 

5.65 

4.14 

5.63 

4.16 

5.61 

4.19 

7 

8 

6.47 

4.70 

6.45 

4.73 

6.43 

4.76 

6.41 

4.79 

8 

9 

7.28 

5.29 

7.26 

5.32 

7.23 

5.35 

7.21 

5.38 

9 

10 

8.09 

5.88 

8.06 

5.91 

8.04 

5.95 

8.01 

5.98 

10 

11 

8.90 

6.47 

8.87 

6.50 

8.84 

6.54 

8.81 

6.58 

11 

12 

9.71 

! 7.05 

9.68 

7.10 

9.65 

7.14 

9.61 

7.18 

12 

13 

10.52 

7.64 

10.48 

7.69 

10.45 

7.73 

10.42 

7.78 

13 

14 

11.33 

8.23 

11.29 

8.28 

11.25 

8.33 

11.22 

8.38 

14 

15 

12.14 

8.82 

12.10 

8.87 

12.06 

8.92 

12.02 

8.97 

15 

16 

12.94 

9.40 

12.90 

9.46 

12.86 

9.52 

12.82 

9.57 

16 

17 

13.75 

9.99 

13.71 

10.05 

13.67 

10.11 

13.62 

10.17 

17 

18 

14.56 

10.58 

14.52 

10.64 

14.47 

10.71 

14.42 

10.77 

18 

19 

15.37 

11.17 

15.32 

11.23 

15.27 

11.30 

15.22 

11.37 

19 

20 

16.18 

11.76 

16.13 

11.83 

16.08 

11.90 

16.03 

11.97 

20 

21 

16.99 

12.34 

16.94 

12.42 

16.88 

12.49 

16.83 

12.56 

21 

22 

17.80 

12.93 

17.74 

13.01 

17.68 

13.09 

17.63 

13.16 

22 

23 

18.61 

13.52 

18.55 

13.60 

18.49 

13.68 

18.43 

13.76 

23 

24 

19.42 

14.11 

19.35 

14.19 

19.29 

14.28 

19.23 

14.36 

24 

25 

20.23 

14.69 

20.16 

14.78 

20.10 

14.87 

20.03 

14.96 

25 

26 

21.03 

15.28 

20.97 

15.37 

20.90 

15.47 

20.83 

15.56 

26 

27 

21.84 

15.87 

21.77 

15.97 

21.70 

16.06 

21.63 

16.15 

27 

28 

22.65 

16.46 

22.58 

16.56 

22.51 

16.65 

22.44 

16.75 

28 

29 

23.46 

17.05 

23.39 

17.15 

23.31 

17.25 

23.24 

17.35 

29 

30 

24.27 

17.63 

24.19 

17.74 

24.12 

17.84 

24.04 

17.95 

30 

31 

25.08 

18.22 

25.00 

18.33 

24.92 

18.44 

24.84 

18.55 

31 

32 

25.89 

18.81 

25.81 

18.92 

25.72 

19.03 

25.64 

19.15 

32 

33 

26.70 

19.40 

26.61 

19.51 

26.53 

19.63 

26.44 

19.74 

33 

34 

27.51 

19.98 

27.42 

20.10 

27.33 

20.22 

27.24 

20.34 

34 

35 

28.32 

20.57 

28.23 

20.70 

28.13 

20.82 

28.04 

20.94 

35 

36 

29.12 

21.16 

29.03 

21 .29 

28.94 

21.41 

28.85 

21.54 

36 

37 

29.93 

21.75 

29.84 

21.88 

29.74 

22.01 

29.65 

22.14 

37 

38 

30.74 

22.34 

30.64 

22.47 

30.55 

22.60 

30.45 

22.74 

38 

39 

31.55 

22.92 

31.45 

23.06 

31.35 

23.20 

31.25 

23.33 

39 

40 

32.36 

23.51 

32.26 

23.65 

32.15 

23.79 

32.05 

23.93 

40 

41 

33.17 

24.10 

33.06 

24.24 

32.96 

24.39 

32.85 

24.53 

41 

42 

33.98 

24.69 

33.87 

24.83 

33.76 

24.98 

33.65 

25.13 

42 

43 

34.79 

25.27 

34.68 

25.43 

34.57 

25.58 

34.45 

25.73 

43 

44 

35.60 

25.86 

35.48 

26.02 

35.37 

26.17 

35.26 

26.33 

44 

45 

36.41 

26.45 

36.29 

26.61 

36.17 

26.77 

36.06 

26.92 

45 

46 

37.21 

27.04 

37.10 

27.20 

36.98 

27.36 

36.86 

27.52 

46 

47 

38.02 

27.63 

37.90 

27.79 

37.78 

27.96 

37.66 

28.12 

47 

48 

38.83 

28.21 

38.71 

28.38 

38.59 

28.55 

38.46 

28.72 

48 

49 

39.64 

28.80 

39.52 

28.97 

39.39 

29.15 

39.26 

29.32 

49 

60 

40.45 

29.39 

40.32 

29.57 

40.19 

29.74 

40.06 

29.92 

50 

<6 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

0 

0 

c 

in 

i a ! 

54 Deg. 

53J Deg. 

53} Deg. 

53} Deg. 

d 

+-» 

O) 

• H 

Q 






























































































TRAVERSE TABLE. 


5 


o 

K • 

CD 

r+- 

P 

36 Deg. 

36$ Deg. 

1 36$ Deg. 

36$ Deg. 

O 

M* 

X 

r** 

p 

n 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

I Dep 

Lat. 

1 Dep. 

i ! 

51 

41.26 

29.98 

41.13 

30.16 

41.00 

30.34 

1 40 86 

130.51 

~51 

52 

42 07 

30.56 

41.94 

30.75 

41.80 

30.93 

41 67 

31.11 

52 

53 

42.88 

31.15 

42.74 

31.34 

42.60 

31.53 

42.47 

31.71 

53 

54 

43.69 

31.74 

43.55 

31.93 

43.41 

32.12 

43.27 

32.31 

54 

55 

44.50 

32.33 

44.35 

32.52 

44.21 

32.72 

44.07 

32.91 

55 

56 

45.30 

32.92 

45.16 

33.11 

45.02 

33.31 

44.87 

33.51 

56 

57 

46.11 

33.50 

45.97 

33.70 

45.82 

33.90 

45.67 

34.10 

57 

58 

46.92 

34.09 

46.77 

34.30 

46.62 

34.50 

46.47 

34.70 

58 

59 

47.73 

34.68 

47.58 

34.89 

47.43 

35 09 

47.27 

35.30 

59 

6 ° 

48.54 

35.27 

48.39 

35.48 

48.23 

35.69 

48.08 

35.90 

60 

61 

49.35 

35.85 

49.19 

36.07 

49.04 

36.28 

48.88 

36.50 

61 

62 

50.16 

36.44 

50.00 

36.66 

49.84 

36.88 

49.68 

37.10 

62 

63 

50.97 

37.03 

50.81 

37.25 

50.64 

37.47 

50.48 

37.69 

63 

64 

51.78 

37.62 

51.61 

37.84 

51.45 

38.07 

51.28 

38.29 

64 

65 

52.59 

38,21 

52.42 

38.44 

52.25 

38.66 

52.08 

38.89 

65 

66 

53.40 

38.79 

53.23 

39.03 

j 53.05 

39.26 

52.88 

39.49 

66 

67 

54.20 

39.38 

54.03 

39.62 

53.86 

39.85 

53.68 

40.09 

67 

68 

55.01 

39.97 

54.84 

40.21 

54.66 

40.45 

54.49 

40.69 

68 

69 

55.82 

40.56 

55.64 

40.80 

55.47 

41.04 

55.29 

41.28 

69 

70 

56.63 

41.14 

56.45 

41.39 

56.27 

41.64 I 

56.09 

41.88 

70 

71 

57.44 

41.73 

57.26 

41.98 

57.07 

42.23 

56.89 

42.48 

71 

72 

58.25 

42.32 

58.06 

42.57 

57.88 

42.83 ! 

57.69 

43.08 

72 

73 

59.06 

42.91 

58.87 

43.17 

58.68 

43.42 

58.49 

43.68 

73 

74 

59.87 

43.50 

59.68 

43.76 

59.49 

44.02 

59.29 

44.28 

74 

75 

60.68 

44.08 

60.48 

44.35 

60.29 

44.61 

60.09 

44.87 

75 

76 

61.49 

44.67 

61.29 

44.94 

61.09 

45.21 

60.90 

45.47 

76 

77 

62.29 

45.26 

62.10 

45.53 

61.90 

45.80 

61.70 

46.07 

77 

78 

63.10 

45.85 

62.90 

46.12 

62.70 

46.40 

62.50 

46.67 

78 

79 

63.91 

46.43 

63.71 

46.71 

63.50 

46.99 

63.30 

47.27 

79 

80 

64.72 

47.02 

64.52 

47.30 

64.31 

47.59 

64.10 

47.87 

80 

81 

65.53 

47.61 

65.32 

47.90 

65.11 

48.18 

64.90 

48.46 

81 

82 

66.34 

48.20 

66.13 

48.49 

65.92 

48.78 

65.70 

49.06 

82 

83 

67.15 

48.79 

66.93 

49.08 

66.72 

49.37 

66.50 

49.66 

83 

84 

67.96 

49.37 

67.74 

49.67 

67.52 

49.97 

67.31 

50.26 

84 

85 

68.77 

49.96 

68.55 

50.26 

68.33 

50.56 

68.11 

50.86 

85 

86 

69.58 

50.55 

60.35 

50.85 

69.13 

51.15 

68.91 

51.46 

86 

87 

70.38 

51.14 

70.16 

51.44 

69.94 

51.75 

69.71 

52.05 

87 

88 

71.19 

51.73 

70.97 

52.04 

70.74 

52.34 

70.51 

52.65 

88 

89 

72.00 

52.31 

71.77 

52.63 

71.54 

52.94 

71.31 

53.25 

89 

90 

72.81 

52.90 

72.58 

53.22 

72.35 

53.53 

72.11 

53.85 

90 

91 

73.62 

53.49 

73.39 

53.81 

73.15 

54.13 

72.91 

54.45 

91 

92 

74.43 

54.08 

74.19 

54.40 

73.95 

54.72 

73.72 

55.05 

92 

93 | 

75.24 

54.66 

75.00 

54.99 

74.76 

55.32 

74.52 

55.64 

93 

94^ 

76.05 

55.25 

75.81 

55.58 

75.56 

55.91 

75.32 

56.24 

94 

1 95 , 

76 86 

55.84 

76.61 

56.17 

76.37 

56.51 

76.12 

56.84 

95 

96 

77.67 

56.43 

77.42 

56.77 

77.17 

57.10 

76.92 

57.44 

96 

97 

78.47 

57.02 

78.23 

57.36 

77.97 

57.70 

77.72 

58.04 

97 

98 

79.28 

57.60 

79.03 

57.95 

78.78 

58.29 

78.52 

58.64 

98 

99 

80.09 

58.19 

79.84 

58.54 

79.58 

58.89 

79-32 

59.23 

99 

100 

80.90 

58.78 

80.64 

59.13 

80.39 

59.48 

80.13 

59.83 

100 

03 

V 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

Lat. 

© 

© 

c 

a 

«-» 

m 

Q 

54 Deg. 

53| Deg. 

53$ Deg. 

53$ Deg. 

C£ 

a 




























































































































76 


TRAVERSE TABLE. 


c 
*“* * 

% 

to 

2 

37 Deg. 

37* Deg. 

37i Deg. 

37| Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

1 

0.80 

0.60 

0.80 

0.61 

0.79 

0.61 

0.79 

0.61 


o 

*4 

1 .00 

1.20 

1.59 

1.21 

1.59 

1.22 

1.58 

1.22 

2 

3 

2.40 

l.Sl 

2.39 

1.82 

2.38 

1 .83 

2.37 

1.84 

3 

4 

3. 19 

2.41 

3.18 

2.42 

3.17 

2 43 

3.16 

2.45 

4 

5 

3.39 

3.01 

3.98 

3.03 

3.97 

3.04 : 

3.95 

3.06 

•> 

6 

] 4.79 

3.61 

4.78 

3 63 

4.76 

3.65 

4.74 

3.67 

G 

i 

5.59 

4.21 

5.57 

4.24 

5.55 

4.26 

5.53 

4.29 

7 

8 

0.39 

4.81 

0.37 

4.84 

6.35 

4.87 

6.33 

4.90 

8 

9 

7. 19 

5.42 

7.16 

5 45 

7.14 

5.48 

7.12 

5.51 

9 

10 

7.99 

0.02 

7.98 

6.05 

7.93 

6.09 

7.91 

6.12 

10 

11 

8.78 

6.62 

8.70 

6.66 

8.73 

6.70 

8.70 

6.73 

11 

12 

9.58 

7.22 

9.55 

7.26 

9.52 

7.31 

9.49 

7.35 

12 

13 

10.33 

7.82 

10.35 

7.87 

10.31 

7.91 

10.28 

7.96 

13 

14 

11.18 

8.43 

11.14 

• 8.47 

11.11 

8.52 

11.07 

8.57 

14 

13 

11.98 

9.03 

11.94 

9.08 

11.90 

9.13 

11.86 

9.18 

15 

16 

12.78 

9.63 

12.74 

9.68 

12.09 

9.74 

12.65 

9.80 

10 

17 

13.58 

10.23 

13.53 

10.29 

13.49 

10.35 

13.44 

10.41 

17 

18 

14.38 

10.83 

14.33 

10.90 

14.28 

10.96 

14.23 

11.02 

18 

19 

15.17 

11.43 

15.12 

11.50 

15.07 

11.57 

15.02 

11.63 

19 

20 

15.97 

12.04 

15.92 

12.11 

15.87 

12.18 

15.81 

12.24 

20 

21 

16.77 

12.04 

16.72 

12.71 

16.66 

12.78 

16.60 

12.86 

21 

22 

17.57 

13.24 

17.51 

13.32 

17.45 

13.39 

17.40 

13.47 

22 

23 

18.37 

13.84 

18.31 

13.92 

18.25 

14.00 

18.19 

14.08 

23 

24 

19.17 

14.44, 

19.10 

14.53 

19.04 

14.61 

18.98 

14.69 

24 

25 

19.97 

15.05 

19.90 

15.13 

19.83 

15.22 

19.77 

15.31 

25 

26 

20.76 

15.65 

20.70 

15.74 

20.63 

15.83 

20.56 

15.92 

26 

27 

21.56 

16.25 

21.49 

16.34 

21.42 

16.44 

21.35 

16.53 

27 

23 

22.33 

16.85 

22.29 

16.95 

22.21 

17.05 

22.14 

17.14 

28 

29 

23.16 

17.45 

23.08 

17.55 

23.01 

17.65 

22.93 

17.75 

29 

30 

23.96 

18.05 

23.83 

18.16 

23.80 

18.26 

23.72 

18.37 

30 

o 1 

24.76 

18.06 

24.68 

18.76 

24.59 

18.87 

24.51 

18.98 

31 

32 

25.56 

19.26 

25.47 

19.37 

25.39 

19.48 

25.30 

19.59 

32 

33 

20.35 

19.80 

26.27 

19.97 

26.18 

20.09 

20.09 

20.20 

33 

34 

27.15 

20.40 

27.06 

20.58 

26.97 

20.70 

26.88 

20.82 

34 

35 

27.95 

21.00 

27.86 

21.19 

27.77 

21.31 

27.67 

21.43 

35 

36 

28.75 

21.67 

2S.66 

21.79 

23.56 

21.92 

28.46 

22.04 

36 

37 

29.55 

22.27 

29.45 

22.40 

29.35 

22.52 

29.26 

22.65 

37 

38 

30.35 

22.87 

30.25 

23.00 

30.15 

23.13 

30.05 

23.26 

3S 

39 

31.15 

23.47 

31.04 

23.61 

30.94 

23.74 

30.84 

23.88 

39 

40 

31.95 

24.07 

31.84 

24.21 

31.73 

24.35 

31.63 

24.49 

40 

41 

32.74 

24.67 

32.64 

24.82 

32 53 

24.90 

32.42 

25. 10 

41 

42 

33.54 

25.28 

33.43 

25.42 

33 32 

25.57 

33.21 

25.71 

42 

43 

34.34 

25.88 

34.23 

26.03 

34.11 

26.18 

34.00 

26.33 

43 

44 

35.14 

20.48 

35.02 

26.63 

34.91 

20.79 

34.79 

26.94 

44 

45 

35.94 

27 .08 

35.82 

27.24 

35.70 

27.39 

35.58 

27.55 

45 

40 

36.74 

27,68 

36.62 

27.84 

36.49 

28.00 

30.37 

28.16 

40 

47 

37.54 

28.29 

37.41 

28.45 

37.29 

28.01 

37.16 

28.77 

47 

48 

33.33 

23.89 

38.21 

29.05 

38.08 

29.22 

37.95 

29.39 

48 

49 

39.13 

29.49 

39.00 

29.60 

38.87 

29.83 

38.74 

30.00 

49 

50 

39.93 

30.09 

39.80 

30.20 

39.67 

30.44 

39.53 

30.01 

50 

6 

o 

p 

Dep. 

Lat. 

Dep. 

Liit. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

o 

** 

SJ 

«-> 

r n 

—\ 

53 Deg. 

52| Deg. 

52£ Deg 

52 \ Dog. 

cd 

.2 

Q 







































































































TRAVERSE TABLE 


77 


t 


“T°- 









~1 

© 

CD 

«-* 

P 

3* Deg. 

37* Deg. 

37 £ Deg. 

373 Deg. 

m 

9 * 

3 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

M 

S 

I . * 

51 

40.73 

30.69 

40.60 

30.87 

40.46 

31.05 

40.33 

31.22 

' 51 

52 

41.53 

31.29 

41.39 

31.48 

41.25 

31.66 

41.12 

31.84 

52 

53 

42.33 

31.90 

42.19 

32.08 

42.05 

32.26 

41.91 

32.45 

53 

54 

43.13 

32.50 

42.98 

32.69 

42.84 

32.87 

42.70 

33.0G 

54 

55 

43.92 

33.10 

43.78 

33.29 

43.63 

33.48 

43.49 

33.67 

55 

56 

44.72 

33.70 

44.58 

33.90 

44.43 

34.09 

44.28 

34.28 

56 

57 

45.52 

34.30 

45.37 

34.50 

45.22 

34.70 

45.07 

34.90 

57 

58 

46.32 

34.91 

46.17 

35.11 

46.01 

35.31 

45.86 

35.51 

58 

59 

47.12 

35.51 

46.96 

35.71 

46.81 

35.92 

46.65 

36.12 

59 

60 

47.92 

36.11 

47.76 

36.32 

47.60 

36.53 

47.44 

36.73 

60 

61 

48.72 

36.71 

48.56 

36.92 

48.39 

37.13 

48.23 

37.35 

61 

62 

49.52 

37.31 

49.35 

37.53 

49.19 

37.74 

49.02 

37.96 

62 

63 

50.31 

37.91 

50.15 

38.13 

49.98 

38.35 

49.81 

38.57 

63 

64 

51.11 

38.52 

50.94 

38.74 

50.77 

38.96 

50.60 

39.18 

64 

65 

51.91 

39.12 

51.74 

39.34 

51.57 

39.57 

51.39 

39.79 

65 

66 

52.71 

39.72 

52.54 

39.95 

52.36 

40.18 

52.19 

40.41 

66 

67 

53.51 

40.32 

53.33 

40.55 

53.15 

40.79 

52.98 

41.02 

67 

68 

54.31 

40.92 

54.13 

41.16 

53.95 

41.40 

53.77 

41.63 

G 8 

69 

55.11 

41.53 

54.92 

41.77 

54.74 

42.00 

54.56 

42.24 

G9 

70 

05.90 

42.13 

55.72 

42.37 

55.53 

42.61 

55.35 

42.86 

70 

71 

56.70 

42.73 

56.52 

42.98 

56.33 

43.22 

56.14 

43.47 

'71 

72 

57.50 

43.33 

57.31 

43.58 

57.12 

43. S3 

56.93 

44.08 

72 

73 

58.30 

43.93 

58.11 

44.19 

57.91 

44.44 

57.72 

44.69 

73 

74 

59,10 

44.53 

58.90 

44.79 

58.71 

45.05 

58.51 

45.30 

74 

75 

59.90 

45.14 

59.70 

45.40 

59.50 

45.66 

59.30 

45.92 

75 

76 

GO. 70 

45.74 

60.50 

46.00 

60.29 

46.27 

60.09 

46.53 

76 

77 

61.49 

46.34 

61.29 

46.61 

61.09 

46.87 

60.88 

47.14 

77 

78 

62.29 

46.94 

62.09 

47.21 

61.88 

47.48 

61.67 

47.75 

78 

79 

63.09 

47.54 

62.88 

47.82 

62.67 

48.09 

62.46 

48.37 

79 

80 

63.89 

48.15 

63.68 

48.42 

63.47 

48.70 

63.20 

48.98 

80 

81 

64.69 

48.75 

64.48 

49.03 

64.26 

49.31 

64.05 

49.59 

81 

82 

65.49 

49.35 

65.27 

49,63 

65.05 

49.92 

64.84 

50.20 

82 

83 

66.29 

49.95 

66.07 

50.24 

65.85 

50.53 

65.63 

50.81 

83 

84 

67.09 

50.55 

66.86 

50.84 

66.64 

51.14 

66.42 

51.43 

84 

85 

67.88 

51.15 

67.66 

51.45 

67.43 

51.74 

67.21 

52.04 

85 

86 

68.68 

51.76 

68.46 

52.06 

68.23 

52.35 

68.00 

52.65 

86 

87 

69.48 

52.36 

69.25 

52.66 

69.02 

52.96 

68.79 

53.26 

87 

88 

70.28 

52.96 

70.05 

53.27 

69.82 

53.57 

69.58 

53.88 

88 

89 

71.08 

53.56 

70.84 

53.87 

70.61 

54.18 

70.37 

54.49 

89 

90 

71.88 

54.16 

71.64 

54.48 

71.40 

54.79 

71.16 

55.10 

90 

91 

72.68 

54.77 

72.44 

55.08 

72.20 

55.40 

71.95 

55.71 

91 

92 

73.47 

55.37 

73.23 

55.69 

72.99 

56.01 

72.74 

56.32 

92 

93 

74.27 

55.97 

74.03 

56.29 

73.78 

56.61 

73.53 

56.94 

93 

94 

75.07 

56.57 

74.82 

56.90 

74.58 

57.22 

74.32 

57.55 

94 

95 

75.87 

57.17 

75.62 

57.50 

75.37 

57.83 

75.12 

58.16 

95 

96 

76.67 

57.77 

76.42 

58.11 

76.16 

58.44 

75 91 

58.77 

96 

97 

77 . 47 

58.38 

77.21 

58.71 

76.96 

59.05 

76 70 

59.39 

97 

98 

78.27 

58.98 

78.01 

59.32 

77.75 

59.66 

77.49 

60.00 

98 

99 

79.06 

59.58 

78.80 

59.92 

78.54 

60.27 

78.28 

60.61 

99 

100 

79.86 

60.18 

79.60 

60.53 

79.34 

60.88 

79.07 

61.22 

100 

6 

o 

S3 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

0 

0 

c 

*-» 

CO 

• H 

Q 

53 Deg. 

52f Deg. 

52£ Deg. 

52^ Deg. 

d 

«-> 

CO • 

■ •—* 

Q 


24 


/ 





































































































78 


TRAVERSE TABLE 


| Distance.! 

32 Dog. 

38.} Deg. 

38} Deg. 

38} Deg. 

D 

5T 

r* 

p3 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

ft 

• 

1 

0.79 

0.62 

0.79 

0.62 

0.78 

0.62 

0.78 

0.63 

1 

2 

1.58 

1.23 

1.57 

1.24 

1.57 

1.24 

1.56 

1.25 

2 

3 

2.36 

1.85 

2.36 

1.86 

2.35 

1.87 

2.34 

1.88 

3 

4 4; 

3.15 

2.46 

3.14 

2.48 

3.13 

2.49 

3.12 

2.50 

4 

5 

3.94 

3.08 

3.93 

3.10 

3.91 

3 11 

3.90 

3.13 

5 

C 

4.73 

3.69 

4.71 

3.71 

4.70 

3.74 

4.68 

3.76 

3 

7 

5.52 

4.31 

5.50 

4.33 

5.48 

4.36 

5.46 

4.38 

7 

8 

6.30 

4.93 

6.28 

4.95 

6.26 

4.98 

6.24 

5.01 

3 

9 

7.09 

6 54 

7.07 

5.57 

7.04 

5.60 

7.02 

5.63 

9 

10 

7.88 

6.16 

7.85 

6.19 

7.83 

G.23 

7.80 

6.26 | 

n 

11 

8.67 

6.77 

8.64 

6.81 

8.61 

6.85 

8.58 

6.89 i 

ii 

12 

9.46 

7.39 

9.42 

7.43 

9.39 

7.47 

9.36 

7.51 

12 

13 

10.24 

8.00 

10.21 

8.05 

10.17 

8.09 

10.14 

8.14 

13 

14 

11.03 

8.62 

10.99 

8.67 

10.96 

8.72 | 

10.92 

8.76 

14 

15 

11.82 

9.23 

11.78 

9.29 

11.74 

9.34 

11.70 

9.39 

15 

16 

12.61 

9.85 

12.57 

9.91 

12.52 

9.96 

12.48 

10.01 

16 

17 

13.40 

10.47 

13.35 

10.52 

13.30 

10.58 

13.26 

10.64 

17 

18 

14.18 

11.08 

14.14 

11.14 

14.09 

11.21 

14.04 

11.27 

18 

19 

14.97 

11.70 

14.92 

11.76 

14.87 

11.83 

14.82 

11.89 

19 

20 

15.76 

12.31 

15.71 

12.38 

15.65 

12.45 

15.60 

12.52 

20 

21 

16.55 

12.93 

16.49 

13.00 

16.43 

13.07 

16.38 

13.14 

21 

22 

17.34 

13.54 

17.28 

13.62 

17.22 

13.70 

17.16 

13.77 

22 

23 

18.12 

14.16 

18.06 

14.24 

18.00 

14.32 

17.94 

14.40 

23 

24 

18.91 

14.78 

18.85 

14.86 

18.78 

14.94 

18.72 

15.02 

24 

25 

19.70 

15.39 

19.63 

15.48 

19.57 

15.56 

19.50 

15.65 

25 

26 

20.49 

16.01 

20.42 

16.10 

20.35 

16.19 

20.28 

16.27 

26 

27 

21.28 

16.62 

21.20 

16.72 

21.13 

16.8] 

21.06 

16.90 

27 

28 

22.06 

17.24 

21.99 

17.33 

21.91 

17.43 

21.84 

17.53 

28 

29 

22.85 

17.85 

22.77 

17.95 

22.70 

18.05 

22.62 

18.15 

29 

30 

23.64 

18.47 

23.56 

18.57 

23.48 

18.68 

23.40 

18.78 

30 

31 

24.43 

19.09 

24.34 

19.19 

24.26 

19.30 

24.18 

19.40 

31 

32 

25.22 

19.70 

25.13 

19.81 

25.04 

19.92 

24.96 

20.03 

32 

33 

26.00 

20.32 

25.92 

20.43 

25.83 

20.54 

25.74 

20.66 

33 

34 

26.79 

20.93 

26.70 

21.05 

26.61 

21.17 

26.52 

21.28 

34 

35 

27.58 

21.55 

27.49 

21.67 

27.39 

21.79 

27.30 

21.91 

35 

36 

28.37 

22.16 

28.27 

22.29 

28.17 

22.41 

28.08 

22.53 

36 

37 

29.16 

22.78 

29.06 

22.91 

28.96 

23.03 

28.86 

23.16 

37 

38 

29.94 

23.40 

29.84 

23.53 

29.74 

23.66 

29.64 

23.79 

38 

39 

30.73 

24.01 

30.63 

24.14 

30.52 

24.28 

30.42 

24.41 

39 

40 

31.52 

24.63 

31.41 

24.76 

31.30 

24.90 

31.20 

25.04 

40 

41 

32.31 

25.24 

32.20 

25.38 

32.09 

25.52 

31.98 

25.66 

41 

42 

33.10 

25.86 

32.98 

26.00 

32.87 

26.15 

32.76 

26.29 

42 

43 

i33.88 

26.47 

33.77 

26.62 

33.65 

26.77 

33.53 

26.91 

43 

44 

34.67 

27.09 

34.55 

27.24 

34.43 

27.39 

34.31 

27.54 

44 

45 

35 46 

27.70 

35.34 

27.86 

35.22 

28.01 

35.09 

28.17 

45 

46 

36.25 

28.32 

36.12 

28.48 

36.00 

28.64 

35.87 

28.79 

46 

47 

37.04 

28.94 

36.91 

29.10 

36.78 

29 26 

36.65 

29.42 

! 47 

48 

37.82 

29.55 

37.70 

29.72 

37.57 

29.88 

37.43 

30.04 

1 48 

49 

38.61 

30.17 

38.48 

30.34 

38.35 

30.50 

38.21 

30.67 

l 49 

50 

39.40 

30.78 

39.27 

30.95 

39.13 

31 13 

38.99 

31.30 

50 

g 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Pen. 

I 

Lat. 

1 ir 

1 5 

li 

52 Deg. 

61} Deg. 

51} Deg. 

51} 

I _ 


3 

73 

i 

1 

m 

























































































































TRAVERSE TAR I E, 


79 


r 

o 
►— • 

era 

; v 

i 5 

j ® 

38 Deg. 

33J Deg. 

i 

334 Deg. 

33f Deg. 

Distance. 

Lvtl. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Ldti 

Dep. 

51 

40.19 

31.40 

40.05 

31.57 

39.91 

31.75 

39.77 

31.92 

51 

52 

40.98 

32.01 

40.84 

32.19 

40.70 

32.37 

40.53 

32.55 

52 , 

53 

41.76 

32.63 

41.62 

32.81 

41.48 

32.99 

41.33 

33.17 

53* 

) 54 

42.55 

33.25 

42.41 

33.43 

42.26 

33.62 

42.11 

33.80 

54 

65 

43.34 

33.86 

! 43.19 

34.05 

43.04 

34.24 

42.89 

34.43 

55 

56 

44.13 

34.48 

43.98 

34.67 

43.83 

34.86 

43.67 

35.05 

56 

57 

44.82 

35.09 

44.76 

35.29 

44.61 

35.48 

44.45 

35.68 

57 

68 

45.70 

35.71 

45.55 

35.91 

45.39 

36.11 

45.23 

36.30 

58 

: 59 

46.49 

36.32 

46.33 

36.53 

46.17 

36.73 

46.01 

36.93 

59 

| GO 

47.28 

36.84 

47.12 

37.15 

46.96 

37.35 

46.79 

37.56 

60 

; 61 

48.07 

37.56 

47.90 

37.76 

47.74 

37.97 

47.57 

38.18 

61 

i 62 

48.86 

38.17 

48.69 

38.38 

48.52 

38.60 

48.35 

38.81 

62 

1 63 

49.64 

38.79 

49.47 

39.00 

49.30 

39.22 

49.13 

39.43 

63 

i 64 

50.43 

39.40 

50.26 

39.62 

50.09 

39.84 

49.91 

40.06 

64 

65 

51.22 

40.02 

51.05 

40.24 

50.87 

40.46 

50.69 

■10.68 

65 

66 

52.01 

40.63 

51.83 

40.86 

51.65 

41.09 

51.47 

41.3J 

66 

67 

52.80 

41.25 

52.62 

41.48 

52.43 

41.71 

52.25 

41.94 

67 

; 68 

53.58 

41.86 

53.40 

42.10 

53.22 

42.33 

53.03 

42.56 

68 

69 

54.37 

42.48 

54.19 

42.72 

54.00 

42.95 

53.81 

43.19 

69 

1 70 

55.16 

43.10 

54.97 

43.34 

54.78 

43.58 

54.59 

43.81 

70 

1 71 

55.95 

43.71 

55.76 

43.96 

55.57 

44.20 

55.37 

44 44 

71 

72 

56.74 

44.33 

56.54 

44.57 

56.35 

44.82 

56.15 

45 07 

72 

| 73 

57.52 

44.94 

57.33 

45.19 

57.13 

45.44 

56.93 

45.69 

73 

: 74 

58.31 

45.56 

58.11 

45.81 

57.91 

46.07 

57.71 

46.32 

74 

75 

59.10 

46.17 

58.90 

46.43 

58.70 

46.69 

58.49 

46.94 

75 

1 76 

59.89 

46.79 

59.68 

47.05 

59.48 

47.31 

59.27 

47.57 

76 

1 77 

60.68 

47.41 

60.47 

47.67 

60.26 

47.93 

GO 05 

48.20 

77 

/8 

61.46 

48.02 

61.25 

48.29 

61.04 

48.56 

60 83 

48.82 

78 

79 

62.25 

48.64 

62.04 

48.91 

61.83 

49.18 

61.61 

49.45 

79 

: 80 

63.04 

49.25 

62.83 

49.53 

62.61 

49.80 

62.39 

50.07 

80 

“81 

63.83 

49.87 

63.61 

50.15 

63.39 

50.42 

63.17 

50.70 

81 

1 82 

64.62 

50.48 

64.40 

50.77 

64.17 

51.05 

63.95 

51.33 

82 

83 

65.40 

51.10 

65.18 

51.38 

64.96 

51.67 

64.73 

51.95 

83 

84 

66.19 

51.72 

65.97 

52.00 

65.74 

52.29 

65.51 

52.58 

84 

85 

66.98 

52.33 

66.75 

52.62 

66.52 

52.91 

66.29 

53.20 

85 

1 86 

67.77 

52.95 

67.54 

53.24 

67.30 

53.54 

67.07 

53.83 

86 

87 

68.56 

53.56 

68.32 

53.86 

68.09 

54.16 

67.85 

54.46 

87 

88 

69.34 

54.18 

69.11 

54.48 

68.87 

54.78 

68.63 

55.08 

88 

89 

70.13 

54.79 

69.89 

55.10 

69.65 

55.40 

69.41 

55.71 

89 

90 

70.92 

55.41 

70.68 

55.72 

70.43 

56.03 

70.19 

56.33 

90 

91 

71.71 

56.03 

71.46 

56.34 

71.22 

56.65 

70.97 

50.96 

91 

92 

72.50 

56.64 

72.25 

56.96 

72.00 

57.27 

71.75 

57.58 

92 

93 

73.28 

57.26 

73.03 

57.58 

72.7S 

57.89 

72.53 

58.21 

93 

• 94 

74.07 

57.87 

73.82 

58.19 

73.57 

58.52 

73.31 

53.84 

94 

95 

.'4 .86 

58.49 

74.61 

58.81 

74.35 

59.14 

74.09 

59.46 

95 

9G 

75.65 

59.10 

75.39 

59.43 

75.13 

59.76 

74.87 

60 09 1 

96 

97 

76.44 

59.72 

76.18 

60.05 

75.91 

60.38 

75.65 

60 ..71 

97 

98 

77.22 

60.33 

76.96 

60.67 

76.70 

61.01 

76.43 

61.34 

98 

99 

78.01 

60.95 

77.75 

61.29 

77.48 

61.63 

77.21 

61.97 

99 

100 

78.80 

61.57 

78.53 

61.91 

78.26 

62.25 

77.99 

62.59 

100 

• 

© 

© 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• i 

© 

© 

c 

rt 

*-* 

g tn 

5 

52 Deg. 

51f Deg. 

5U Deg. 

5U Deg 

cS 

tD 

5 


























































































































THAVEltSE TAKt.2 


o 

ce 

<-* 

3 

o 

« 

39 Deg. 

39} Deg. 

! 39}- 

1 

Deg. 

39$ Deg. 

£? 

c/> 

c-*- 

C9 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

p 


0.78 

0.63 

0.77 

0.63 

0.77 

0.64 

0.77 

0 64 

1 

2 

1.55 

1.26 

1.55 

1.27 

1.54 

1.27 

1.54 

1.28 

2 

3 

2.33 

1.89 

2.32 

1.90 

2.31 

1.91 

2.31 

1.92 

3 

4 

3.11 

2.52 

3.10 

2.53 

3.09 

2.54 

3.08 

2.56 

4 

5 

3.89 

3.15 

3.87 

3.16 

3.86 

3.18 

3.84 

3.20 

5 

6 

4.66 

3.78 

4.65 

3.80 

4.83 

3.82 

4.61 

3.84 

6 

7 

5.44 

4.41 

5.42 

4.43 

5.40 

4.45 

5.38 

4.48 

7 

8 

6.22 

5.03 

6.20 

5.06 

6.17 

5.09 

6.15 

5.12 

8 

9 

6.99 

5.60 

6.97 

5.69 

6.94 

5.72 

6.92 

5.75 

9 

10 

7.77 

6.29 

7.74 

6.33 

7.72 

6.36 

7.69 

6.39 

10 : 

; 'll 

8.55 

6.92 

8.52 

6.96 

8.49 

7.00 

8.46 

7.03 

11 

12 

9.33 

7.55 

9.29 

7.59 

9.26 

7.63 

9.23 

7.67 

12 \ 

13 

10.10 

8.18 

10.07 

8.23 

10.03 

8.27 

9.99 

8.31 

13 : 

14 

10.88 

8.81 

10.84 

8.86 

10.80 

8.91 

10.76 

8.95 

14 

15 

11.66 

9.44 

11.62 

9.49 

11.57 

9.54 

11.53 

8.59 

15 

16 

12.43 

10.07 

12.39 

10.12 

12.35 

10.18 

12.30 

10.23 

16 

17 

13.21 

10.70 

13.16 

10.76 

13.12 

10.81 

13.07 

10.87 

17 

18 

13.99 

11.33 

13.94 

11.39 

13.89 

11.45 

13.84 

11.51 

18 

19 

14.77 

11.96 

14.71 

12.02 

14 66 

12.09 

14.61 

12.15 

19 

20 

15.54 

12.59 

15.49 

12.65 

15.43 

12.72 

15.38 

12.79 

20 

21 

16.32 

13.22 

16.26 

13.29 

16.20 

13.36 

16.15 

13.43 

21 ; 

22 

17.10 

13.84 

17.04 

13.92 

16.98 

13.99 

16.91 

14.07 

22 

23 

17.87 

14.47 

17.81 

14.55 

17.75 

14.63 

17.68 

14.71 

23 1 

24 

18.65 

15.10 

18.59 

15.18 

18.52 

15.27 

18.45 

15.35 

24 

25 

19.43 

15.73 

19.36 

15.82 

19.29 

15.90 

19.22 

15.99 

25 

26 

20.21 

16.36 

20.13 

16.45 

20.06 

16.54 

19.99 

16.63 

26 

27 

20.98 

16.99 

20.91 

17.08 

20.83 

17.17 

20.76 

17.26 

27 

28 

21.76 

17.62 

21.68 

17.72 

21.61 

17.81 

21.53 

17.90 

28 : 

29 

22.54 

18.25 

22.46 

18.35 

22.38 

18.45 

22.30 

18.54 

29 

30 

23.31 

18.88 

23.23 

18.98 

23.15 

19.08 

23.07 

19.18 

30 

31 

24.09 

19.51 

24.01 

19.61 

23.92 

19.72 

23.83 

19.82 

31 

32 

24.87 

20.14 

24.78 

20.25 

24.69 

20.35 

24.60 

20.46 

32 

33 

25.65 

20.77 

25.55 

20.88 

25.46 

20.99 

25.37 

21.10 

33 1 

34 

26.42 

21.40 

26.33 

21.51 

26.24 

21.63 

26.14 

21.74 

34 

35 

27.20 

22.03 

27.10 

22.14 

27.01 

22.26 

26.91 

22.38 

35 

36 

27.98 

22.66 

27.88 

22.78 

27.78 

22.90 

27.68 

23.02 

36 

37 

28.75 

23.28 

28.65 

23.41 

28.55 

23.53 

28.45 

23.66 

37 

38 

29.53 

23.91 

29.43 

24.04 

29.32 

24.17 

29.22 

24.30 

38 . 

39 

30.31 

24.54 

30.20 

24.68 

30.09 

24.81 

29.98 

24.94 

39 

40 

31.09 

25.17 

30.98 

25.31 

30.86 

25.44 

30.75 

25.58 

40 

41 

31.86 

25.80 

31.75 

25.94 

31.64 

26.08 

31.52 

26.22 

41 

42 

32.64 

26.43 

32.52 

26.57 

32.41 

26.72 

32.29 

26.86 

42 

43 

33.42 

27.06 

33.30 

27.21 

33.18 

27.35 

33.06 

27.50 

43 

44 

34.19 

27.69 

34.07 

27.84 

33.95 

27.99 

33.83 

28.11 

14 

45 

34.97 

28.32 

34.85 

28.47 

34.72 

28.62 

34.60 

28.77 

15 

46 

35.75 

28.95 

35.62 

29.10 

35.49 

29.26 

35.37 

29.41 

46 

47 

36.53 

29.58 

36.40 

29.74 

36.27 

29.90 

36.14 

30.05 

47 

48 

37.30 

30.21 

37.17 

30.37 

37.04 

30.53 

36.90 

30.69 

48 

49 

38.08 

30.84 

37.95 

31.00 1 

37.81 

31.17 

37.67 

31.33 

49 

50 

38.86 

31.47 

38.72 

31.64 

38.58 

31.80 

38.44 

31.97' 

50 . 

0) 

o 

c 

Dop. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

« 

u 

Ej 

cd 

w 

Q 

51 Deg. 

50f Deg. 

50£ Deg. 

50} Deg. 

cd 

0Q 

• H 

Q , 







































































































TRAVERSE 'TARLE. 


61 


o 

S’ 

c* 

p: 

39 Deg. 

39} Deg. 

39i Deg. 

39f Deg. 

o: 

• 

LC 

r+- 

3 

o 

n 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat* 

Dep. 

S ! 
o ; 
CD j 

tl 

39.63 

32.10 

39.49 

32.27 

39.35 

32.44 

39.21 

32.61 

51 

52 

40.41 

32.72 

40.27 

32.90 

40.12 

33.08 

39.98 

33. 25 

52- 

53 

41.19 

33.35 

41.04 

33.53 

40.90 

33.71 

40.75 

33 89 

53 

54 

41.97 

33.98 

41.82 

34.17 

41.67 

34.35 

41.52 

34.53 

54 

55 

42.74 

34 61 

42.59 

34.80 

42.44 

34.98 

42.29 

35.17 

55 

66 

:43.52 

1 35.24 

43.37 

35.43 

43.21 

35.62 

43.06 

35.81 

56 

67 

1 44.30 

35.87 

44.14 

36.06 

43.98 

36.26 

43.82 

36.45 

57 

68 

45.07 

36.50 

44.91 

36.70 

44.75 

36.89 

44.59 

37.09 

58 

59 

|45.85 

37.13 

45.69 

37.33 

45.53 

37.53 

45.36 

37.73 

59 

60 

I 46.63 

37.76 

46.46 

37.96 

46.30 

38.16 

46.13 

38.37 

60 

61 

47.41 

38.39 

47.24 

38.60 

47.07 

38.80 

46.90 

39.01 

61 

62 

48.18 

39.02 

48.01 

39.23 

47.84 

39.44 

47.67 

39.65 

62 

63 

48.96 

39.65 

48.79 

39.86 

48.61 

40.07 

48.44 

40.28 

63 

64 

49.74 

40.28 

49.56 

40.49 

49.38 

40.71 

49.21 

40.92 

64 

65 

50.51 

40.91 

50.34 

41.13 

50.16 

41.35 

49.97 

41.56 

65 

66 

51.29 

41.54 

51.11 

41.76 

50.93 

41.98 

50.74 

42.20 

66 

67 

52.07 

42.16 

51.88 

42.39 

51.70 

42.62 

51.51 

42.84 

67 

68 

52.85 

42.79 

52.66 

43.02 

52.47 

43.25 

52.28 

43.48 

68 

69 

53.52 

43.42 

53.43 

43.66 

53.24 

43.89 

53.05 

44.12 

69 

70 

54.40 

44.05 

54.21 

44.29 

54.01 

44.53 

53.82 

44.76 

70 

71 

55.18 

44.68 

54.98 

44.92 

54.79 

45.16 

54.59 

45.40 

71 

72 

55.95 

45.31 

55.76 

45.55 

55.56 

45.80 

55.36 

46.04 

72 

73 

56.73 

45.94 

56.53 

46.19 

56.33 

46.43 

56.13 

46.68 

73 

74 

57.51 

46.57 

57.31 

46.82 

57.10 

47.07 

56.89 

47.32 

74 

75 

58.29 

47.20 

58.08 

47.45 

57.87 

47.71 

57.66 

47.96 

75 

76 

59.06 

47.83 

58.85 

48.09 

58.64 

48.34 

58.43 

48.60 

76 

77 

59.84 

48.46 

59.63 

48.72 

59.42 

48.98 

59.20 

49.24 

77 

78 

60.62 

49.09 

60.40 

49.35 

60.19 

49.61 

59.97 

49.88 

78 

79 

61.39 

49.72 

61.18 

49.98 

60.96 

50.25 

60.74 

50.52 

79 

80 

62.17 

50.35 

61.95 

50.62 

61.73 

50.89 

61.51 

51.16 

80 

81 

62.95 

50.97 

62.73 

51.25 

62.50 

51.52 

62.28 

51.79 

81 

82 

63.73 

51 .60 

63.50 

51.88 

63.27 

52.16 

63.04 

52.43 

82 

83 

64.50 

52.23 

64.27 

52.51 

64.04 

52.79 

63.81 

53.07 

83 

84 

65.28 

52.86 

65.05 

53.15 

64.82 

53.43 

64.58 

53.71 

84 

85 

66.06 

53.49 

65.82 

53.78 

65.59 

54.07 

165.35 

54.35 

85 

86 

66.83 

54.12 

66.60 

54.41 

66.36 

54.70 

166.12 

54.99 

86 

87 

67.61 

54.75 

67.37 

55.05 

67.13 

55.34 

66.89 

55.63 

87 

88 

68.39 

55.38 

68.15 

55.68 

67.90 

55.97 

67.66 

56.27 

88 

89 

69.17 

56.01 

68.92 

56.32 

68.67 

56.61 

68.43 

56.91 

89 

90 

69.94 

56.64 

69.70 

56.94 

69.45 

57.25 

69.20 

57.55 

90 

'91 

70.72 

57.27 

70.47 

57.58 

70.22 

57.88 

69.96 

58.19 

91 

92 

71.50 

57.90 

71.24 

58.21 

70.99 

58.52 

70.73 

58.83 

92 

93 

72.27 

58.53 i 

72.02 

58.84 

71.76 

59.16 

71.50 

59.47 

93 

94 

73.05 

59.16 

72.79 

59.47 

72.53 

59.79 

72.27 

60.11 

94 

95 

73.83 

59.79 

73.57 

60.11 

73.30 

60.43 

73.04 

60.75 

95 

96 

74.61 

60.41 

74.34 

60.74 

74.08 

61.06 

73.81 

61.39 

9G; 

97 

75.38 

61.041 

75.12 

61.37 

74.85 

61.70 

74.58 

62.03 

97 

93 

76.16 

61.67 

75.89 

62.01 

75.62 

62.34 

75.35 

62.66 

98 

99 

76.94 

62.30 

76.66 

62.64 

76.39 

62.97 

76.12 

63.30 

99 1 

100 

77.71 

62.93 

77.44 

63.27 

77.16 

63.61 

76.88 

63.94 

lOOf 

<v 

V 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

l 

rJ 

* i 
o 

51 Deg. 

50f Deg. 

50} Deg. 

50} Deg. 

IC 

3*1 













































































































£2 


TRAVERSE TAKLE 


o 

r/i 

r~* 

40 Deg. 

40} Deg. 

40 £ Deg. 

401 Deg. 

Disla 


P 

3 

O 

O 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep, ! 

3 

o 

• 


l 

0.77 

0.64 

0.76 

0.65 

0.76 

0.65 

0.76 

0.65 

1 


2 

1.53 

1.29 

1.53 

1.29 

1.52 

1.30 

1.52 

1.31 

2 


3 

2.30 

1.93 

2.29 

1.94 

2.28 

1.95 

2.27 

1.96 

3 


4 

3.('6 

2.57 

3.05 

2.58 

3.04 

2.60 

3.03 

2.61 

4 


5 

3.83 

3.21 

3.82 

3.23 

3.80 

3.25 

3.79 

3.26 

5 


6 

4.60 

3.86 

4.58 

3.88 

4.56 

3.90 

4.55 

3.92 

6 


7 

5.36 

4.50 

5.34 

4.52 

5.32 

4.55 

5.30 

4.57 

7 


8 

6.13 

5.14 

6.11 

5.17 

6.08 

5.20 

6.06 

5.22 

8 


9 

6.89 

5.79 

6.87 

5.82 

6.84 

5.84 

6.82 

5-87 

9 


10 

7.66 

6.43 

7.63 

6.46 

7.60 

6.49 

7.58 

6.53 

10 


11 i 

8.43 

7.07 

8.40 

7.11 

8.36 

7.14 

8.33 

7.18 

11 


12 

9.19 

7.71 

9.16 

7.75 

9.12 

7.79 

9.09 

7.83 

12 


13 

9.96 

8.36 

9.92 

8.40 

9.89 

8.44 

9.85 

8.49 

.3 


14 

10.72 

9.00 

10.69 

9.05 

10.65 

9.09 

10.61 

9.14 

14 


15 

11.49 

9.64 

11.45 

9.69 

11.41 

9.74 

11.36 

9.79 

15 


16 

12.26 

10.28 

12.21 

10.34 

12.17 

10.39 

12.12 

10.44 

16 


17 

13.02 

10.93 

12.97 

10.98 

12.93 

11.04 

12.88 

11.10 

17 


18 

13.79 

11.57 

13.74 

11.63 

13.69 

11.69 

13.64 

11.75 

18 


19 

14.55 

12.21 

14.50 

12.28 

14.45 

12.34 

14.39 

12.40 

19 


20 

15.32 

12.86 

15.26 

12.92 

15.21 

12.99 

15.15 

13.06 

20 


21 

16.09 

13.50 

16.03 

13.57 

15.97 

13.64 

15.91 

13.71 

21 


22 

16.85 

14.14 

16.79 

14.21 

16.73 

14.29 

16.67 

14.36 

22 


23 

17.62 

14.78 

17.55 

14.86 

17.49 

14.94 

17.42 ' 

15.01 

23 


24 

18.39 

15.43 

18.32 

15.51 

18.25 

15.59 I 

18.18 

15.67 

24 


25 

19.15 

16.07 

19.08 

16.15 

19.01 

16.24 

18.94 

16.32 

25 


• 26 

19.92 

16.71 

19.84 

16.80 

19.77 

16.89 

19.70 

16.97 

26 


27 

20.68 

17.36 

20.61 

17.45 

20.53 

17.54 [ 

20.45 

17.62 

27 


28 

21.45 

18.00 

21.37 

18.09 

21.29 

IS.18 

21.21 

18.28 

28 


29 

22.22 

18.64 

22.13 

18.74 

22.05 

18.83 

21.97 

18.93 

29 


30 

22.98 

19.28 

22.90 

19.38 

22.81 

19.48 

22.73 

19.58 

30 


31 

23.75 

19.93 

23.66 

20.03 

23.57 

20.13 

23.48 

20.24 

31 


32 

24.51 

20.57 

24.42 

20.68 

24.33 

20.78 

124.24 

20.89 

32 

' 

33 

25.28 

21.21 

25.i 9 

21.32 

25.09 

21.43 

25.00 

21.54 

33 

\ 

34 

26.05 

21.85 

25.95 

21.97 

25.85 

22.08 

125.76 

22.19 

34 


35 

26.81 

22.50 

26.71 

22.61 

26.61 

22.73 

26.51 

22.85 

35 


36 

27.58 

23.14 

27.48 

23.26 

27.37 

23.38 

27.27 

23.50 

36 


37 

28.34 

23.78 

28.24 

23.91 

28.13 

24.03 

28.03 

24.15 

37 


38 

29.11 

24.43 

29.00 

24.55 

28.90 

24.68 

28.79 

24.80 

38 


1 39 

29.88 

25.07 

29.77 

25.20 

29.66 

25.33 

29.54 

25.46 

39 


40 

30.64 

25.71 

30.53 

25.84 

30.42 

25.98 

30.30 

26.11 

40 

\ 

41 

31.41 

26.35 

31.29 

26.49 

31.18 

26.03 

31.06 

26.76 

41 


42 

32.17 

27.00 

32.06 

27.14 

31.94 

27.28 

31.82 

27.42 

42 


43 

32.94 

27.64 

32.82 

27.78 

32.70 

27.93 

32.58 

28.07 

43 


44 

33.71 

28.28 

33.58 

28.43 

33.46 

28.58 

33.33 

28.72 

44 


45 

34.47 

28.93 

34.35 

29.08 

34.22 

29.23 

34.09 

29.37 

45 


46 

35.24 

29.57 

35.11 

29.72 

34.98 

29.87 

34.85 

30.03 

46 


47 

36.00 

30.21 

35.87 

30.37 

35.74 

30.52 

35.61 

30.68 

47 


48' 

36.77 

30.85 

36.64 

31.01 

36.50 

31.17 

36.36 

31.33 

48 


49 

37.54 

31.50 

37.40 

31.66 

37.26 

31.82 

37.12 

31.99 

49 


50 

38.30 

32.14 

38.16 

32.31 

38.02 

!32.47 

37.88 

!32.64 

50 

*> 

o' 

V 

e 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

c 

V 

c 


S' ♦-» 

S 

It *H 

l ^ 

50 Deg. 

49$ Deg. 

49} 

1 

Deg. 

49} Deg. 

cd 

w 

• h 

G 



































































































































Tit A VERSE TABLE 


83 


o 

to 

P 

40 De^, 

40} Deg. 

40} Deg. 

40} Deg. 

Distance. 

5 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

39.07 

32.78 

38.92 

32.95 

38.78 

33.12 

38.64 

33.29 

51 

52 

39.83 

33.42 

39.69 

33.60 

39.54 

33.77 

39.39 

33.94 

52 

53 

40.60 

'34.07 

40.45 

34..24 

40.30 

34.42 

40.15 

34.60 

53 

54 

41.37 

34.71 

41.21 

34.89 

41.06 

35.07 

40.91 

35.25 

54 

55 

42.13 

35.35 

41.98 

35.54 

41.82 

35.72 

41.67 

35.90 

55 

56 

42.90 

36.00 

42.74 

36.18 

42.58 

36.37 

42.42 

36.55 

56 

57 

43.66 

36.64 

43.50 

36.83 

43.34 

37.02 

43.18 

37.21 

57 

58 

44.43 

37.28 

44.?; 

37.48 

44.10 

37.67 

43.94 

37.86 

58 

59 

45.20 

37.92 

45.03 

38.12 

44.86 

38.32 

44.70 

38.51 

59 

60 

45.96 

38.57 

45.79 

38.77 

45.62 

38.97 

45.45 

39.17 

60 

61 

46.73 

39.21 

46.56 

39.41 

46.38 

39.62 

46.21 

39.82 

61 

62 

47.49 

39.85 

47.32 

40.06 

47.15 

40.27 

46.97 

40.47 

62 

63 

48.26 

40.50 

48.08 

40.71 

47.91 

40.92 

47.73 

41.12 

63 

64 

49.03 

41.14 

48.85 

41.35 

48.67 

41.56 

48.48 

41.78 

64 

65 

49.79 

41.78 

49.61 

42.00 

49.43 

42.21 

49.24 

42.43 

65 

66 

50.56 

42.42 

50.37 

42.64 

50.19 

42.86 

50.00 

43.08 

66 

67 

51.32 

43.07 

51.14 

43.29 

50.95 

43.51 

50.76 

43.73 

67 

68 

52.09 

43.71 

51.90 

43.94 

51.71 

44.16 

51.51 

44.39 

68 

69 

52.86 

44.35 

52.66 

44.58 

52.47 

44.81 

52.27 

45.04 

69 

70 

53.62 

45.00 

53.43 

45.23 

53.23 

45.46 

53.03 

45.69 

70 

71 

54.39 

45.64 

54.19 

45.87 

53.99 

46.11 

53.79 

46.35 

71 

72 

55.16 

46.28 

54.95 

48.52 

54.75 

46.76 

54.54 

47.00 

72 

73 

55.92 

46.92 

55.72 

47.17 

55.51 

47.41 

55.30 

47.65 

73 

74 

56.69 

47.57 

'56.48 

47.81 

56.27 

48.06 

56.06 

48.30 

74 

75 

57.45 

48.21 

57.24 

48.46 

57.03 

48.71 

56.82 

48.96 

75 

76 

58.22 

48.85 

58.01 

49.11 

57.79 

49.36 

57.57 

49.61 

76 

77 

58.99 

49.49 

58.77 

49.7,5 

58.55 

50.01 

58.33 

50.26 

77 

78 

59.75 

50.14 

59.53 

50.40 

59.31 

50.66 

59.09 

50.92 

78 

79 

60.52 

50.78 

00.30 

51.04 

60.07 

51.31 

59.85 

51.57 

79 

80 

61.2S 

51.42 

61.06 

51.69 

60.83 

51.96 

60.61 

52.22 

80 

81 

62.05 

52.07 

61.82 

52.34 

61.59 

52.61 

61.36 

52.87 

81 

82 

62.82 

52.71 

62.59 

52.98 

62.35 

53.25 

62.12 

53.53 

82 

83 

63.58 

53.35 

63.35 

53.63 

63.11 

53.90 

62.88 

54.18 

83 

84 

64.35 

53.99 

64.11 

54.27 

63.87 

54.55 

63.64 

54.83 

84 

85 

65.11 

54.64 

64.87 

54.92 

64 • 63 

55.20 

64.39 

55.48 

85 

86 

65.88 

55.28 

65.64 

55.57 

65-39 

55.85 

65.15 

56.14 

86 

87 

66.65 

55.92 

66.40 

56.21 

66.16 

56.50 

65.91 

56.79 

87 

88 

67.41 

56.57 

67.16 

56.86 

66.92 

57.15 

66.67 

57.44 

88 

89 

68.18 

57.21 

67.93 

57.50 

67.68 

57.80 

67.42 

58.10 

89 

90 

68.94 

57.85 

68.69 

58.15 

68.44 

58.45 

68.18 

58.75 

90 

91 

69.71 

58.49 

69.45 

58. SO j 

69.20 

59.10 

68.94 

59.40 

91 

92 

70.48 

59.14 

70.22 

59.44 j 

69.96 

59.75 

69.70 

60.05 

92 

93 

71.24 

59.78 

70.93 

60.09 

70.72 

60.40 

70.45 

60.71 

93 

94 

72.01 

60.42 

71.74 

60.74 

71.48 

61.05 

71.21 

61.36 

94 

95 

72.77 

61.06 

72.51 

61.38 

72.24 

61.70 

71.97 

62.01 

95 

96 

73.54 

61.71 

73.27 

62.03 

73.00 

62.35 

72.73 

62.66 

96 

97 

74.31 

62.35 

74.03 

62.67 

73.76 

63.00 

73.48 

63.32 

97 

98 

75.07 

62.99 

74.80 

63.32 

74.52 • 

63.65 

74.24 

63.97 

98 

99 

75.84 

63.64 

75.56 

63.97 

75.28 

64.30 

75.00 

64.62 

99 

100 

76.60 

64.28 

76.32 

64.61 

76.04 

64.94 

75.76 

65 28 

100 

d 

o 

c 

Dep. 

Lat. 

Dep. 

Lat.. 

“ 1 
Dep. 

Lat. 

Dep. 

1 

Lat. 

d 

o 

t: 

ri 

■*-> 

3Q 

• M 

Q 

50 Deg. 

49} Deg. 

49} Deg. 

49} Deg. 

rt 

.2 / 

ii 




























































































































84 


TRAVERSE TABLE 


Distance. 

i 

41 Deg. 

A\\ Deg. 

4H 

Deg. 

i 

41| Deg. 

C 

a 

<-» 

PS 

3 

O 

3 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Ijnt. 

Dep. 

1 

0.75 

0.66 

0.75 

0 .C6 

0.75 

0.66 

0.75 

0 67 

1 

2 

1.51 

1.31 

1.50 

1.32 

1.50 

1.33 

1.49 

1.33 

2 

3 

2.26 

1.97 

2.26 

1.98 

2.25 

1 .99 

2.24 

2.00 

3 

4 

3.02 

2.62 

3.01 

2.64 

3.00 

2.65 

2.98 

2.66 

4 

5 

3.77 

3.28 

3.76 

3.30 

3.74 

3.31 

3.73 

3.33 

5 

6 

4.53 

3.94 

4.51 

3.90 

4.49 

3.98 

4.48 

4.00 

6 

7 

5.28 

4.59 

5.26 

4.62 

5.24 

4.64 

5.22 

4.66 

7 

8 

6.04 

5.25 

6.01 

5.27 

5 99 

5.30 

5.97 

5.33 

8 

9 

6.79 

5.90 

6.77 

5.93 

6.74 

5.96 

6.71 

5.99 

9 

10 

7.55 

6.56 

7.52 

6.59 

7.49 

6.63 

7.46 

6.66 

10 

11 

8.30 

7 99 

8.27 

7.25 

8.24 

7.29 

8.21 

7.32 

11 

12 

9.06 

7.87 

9.02 

7.91 

8.99 

7.95 

8.95 

7.99 

12 

13 

9.81 

8.53 

9.77 

8.57 

9.74 

8.61 

9.70 

8.66 

13 

14 

10.57 

9.18 

10.53 

9.23 

10.49 

9.28 

10.44 

9.32 

14 

15 

11.32 

9.84 

11.28 

9.89 

11.23 

9.94 

11.19 

9.99 

15 

16 

12.08 

10.50 

12.03 

10.55 

11.98 

10.60 

11.94 

10.65 

16 

17 

12.83 

11.15 

12.78 

11.21 

12.73 

11.26 

12.68 

11.32 

17 

18 

13.58 

11.81 

13.53 

11.87 

13.48 

11.93 

13.43 

11.99 

18 

19 

14.34 

12.47 

14.28 

12.53 

14.23 

12.59 

14.18 

12.65 

19 

20 

15.09 

13.12 

15.04 

13.19 

14.98 

13.25 

14.92 

13.32 

20 

21 

15.85 

13.78 

15.79 

13.85 

15.73 

13.91 

15.67 

13.98 

21 

22 

16.60 

14.43 

16.54 

14.51 

16.48 

14.58 

16.41 

14.65 

22 

23 

17.36 

15.09 

17.29 

15.16 

17.23 

15.24 

17.16 

15.32 

23 

24 

18.11 

15.75 

18.04 

15.82 

17.97 

15.90 

17.91 

15.98 

24 

25 

18.87 

16.40 

18.80 

16.48 

18.72 

16.57 

18.65 

16.65 

25 

26 

19.62 

17.06 

19.55 

17.14 

19.47 

17.23 

19.40 

17.31 

26 

27 

20.38 

17.71 

20.30 

17.80 

20.22 

17.89 

20.14 

17.98 

27 

28 

21.13 

18.37 

21.05 

18.46 

20.97 

18.55 

20.89 

18.64 

28 

29 

21.89 

19.03 

21.80 

19.12 

21.72 

19.22 

21.64 

19.31 

29 

30 

22.64 

19.68 

22.56 

19.78 

22.47 

19.88 

22.38 

19.98 

30 

31 

23.40 

20.34 

23.31 

20.44 

23.22 

20.54 

23.13 

20.64 

31 

32 

24.15 

20.99 

24.06 

21.10 

23.97 

21.20 

23.87 

21.31 

32 

33 

24.91 

21.65 

24.81 

21.76 

24.72 

21.87 

24.62 

21.97 

33 

34 

25.66 

22.31 

25.56 

22.42 

25.4.6 

22.53 

25.37 

22.64 

34 

35 

26.41 

22.96 

26.31 

23.08 

26.21 

23.19 

26.11 

23.31 

35 

36 

27.17 

23.62 

27.07 

23.74 

26.96 

23.85 

26.86 

23.97 

36 

37 

27.92 

24.27 

27.82 

24.40 

27.71 

24.52 

27.60 

24.64 

37 

38 

28.68 

24.93 

28.57 

25.06 

28.46 

25.18 

28.35 

25.30 

38 1 

39 

29.43 

25.59 

29.32 

25.71 

29.21 

25.84 

29.10 

25.97 

39 

40 

30.19 

26.24 

30.07 

26.37 

29.96 

26.50 

29.84 

26.64 

40 

41 

30.94 

26.90 

30.83 

27.03 

30.71 

27.17 

30.59 

27.30 

41 

42 

31.70 

27.55 

31.58 

27.69 

31.46 

27.83 

31.33 

27.97 

42 

43 

32.45 

28.21 

32.33 

23.35 

32.21 

28.49 

32.08 

28.63 

43 

44 

33.21 

28.87 

33.08 

29.01 

32.95 

29.16 

32.83 

29.30 

44 

45 

33.96 

29.52 

33.83 

29.67 

33.70 

29.82 

33.57 

29.97 

45 

46 

34.72 

30.18 

34.58 

30.33 

34.45 

30.48 

34.32 

30.63 

46 

47 

35.47 

30.83 

35.34 

30.99 

35.20 

31.14 

35.06 

31.30 

47 

48 

36.23 

31.49 

36.09 

31.65 

35.95 

31.81 

35.81 

31 96 

48 

49 

36.98 

32.15 

36.84 

32.31 

36.70 

32.47 

36.56 

32. 63 

49 

50 

37.74 

32.80 

37.59 

32.97 

37.45 

33.13 

37.30 

33.29 

50 

© 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

c 

08 

00 

Q 

49 Deg. 

48 J Deg. 

48i Deg. 

48 i Deg. 

•d 

+-> 

GO 

• 




































































































TRAVERSE TABLE 


85 


2 

c r/ 

P 

41 Deg. 

4l£ Deg. 

41 i Deg. 

41,f Deg. 

2 

r/i 

<—* 

P 

3 

3 

C9 

Licit. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

5 l 

33.49 

33.46 

38.34 

33.63 

38.20 

33.79 

38.05 

33.96 

51 

52 

39.24 

34.12 

39.10 

34.29 

38.95 

34.46 

38.79 

34.63 

52 

53 

40.00 

34.77 

39.85 

34.95 

39.69 

35.12 

39.54 

35.29 

53 

54 

40.75 

35.43 

40.60 

35.60 

40.44 

35.78 

40.29 

35.96 

54 

55 

41.51 

36.08 

41.35 

36.26 

41.19 

36.44 

41.03 

36.62 

55 

56 

42 26 

36.74 

42.10 

36.92 

41.94 

37.11 

41.78 

37.29 

56 

57 

43 02 

37.40 

42.85 

37.58 

42.69 

37.77 

42.53 

37.96 

57 

53 

43.77 

38.05 

43.61 

38.24 

43.44 

38.43 

43.27 

38.62 

58 

56 

4 4.53 

38.71 

44.36 

38.90 

44.19 

39.09 

44 . 02 

39.29 

59 

6 C 

45.28 

39.36 

45.11 

39.56 

44.94 

39.76 

44.76 

39.95 

60 

61 

46.04 

40.02 

45.86 

40.22 

45.69 

40.42 

45.51 

40.62 

61 

62 

46.79 

40.68 

46.61 

40.88 

46:44 

41.08 

46.26 

41.28 

62 

63 

47.55 

41.33 

47.37 

41.54 

47.IS 

41.75 

47.00 

41.95 

63 

64 

48.30 

41.99 

48.12 

42.20 

47.93 

42.41 

47.75 

42.62 

64 

65 

49.06 

42.64 

48.87 

42.86 

48.68 

43.07 

48.49 

43.28 

65 

66 

49.81 

43.30 

49.62 

43.52 

49.43 

43.73 

49.24 

43.95 

66 

67 

50.57 

43.96 

50.37 

44.18 

50.18 

44.40 

49.99 

44.61 

67 

68 

51.32 

44.61 

51.13 

44.84 

50.93 

45.06 

50.73 

45.28 

68 

69 

52.07 

45.27 

51.88 

45.49 

51.68 

45.72 

51.48 

45.95 

69 

70 

52.83 

45.92 

52.63 

46.15 

52.43 

46.38 

52.22 

46.61 

70 

71 

53.58 

46.58 

53.38 

46.81 

53.18 

47.05 

52.97 

47.28 

71 

72 

54.34 

47.24 

54.13 

47.47 

53.92 

47.71 

53.72 

47.94 

72 

73 

55.09 

47.89 

54.88 

48.13 

54.67 

48.37 

54.46 

48.61 

73 

74 

55.85 

48.55 

55.64 

48.79 

55.42 

49.03 

55.21 

49.28 

74 

75 

56.60 

49.20 

56.39 

49.45 

56.17 

49.70 

55.95 

49.94 

75 

76 

57.36 

49.86 

57.14 

50.11 

56.92 

50.36 

56.70 

50.61 

76 

77 

58.11 

50.52 

57.89 

50.77 

57.67 

51.02 

57.45 

51.27 

77 

78 

58.87 

51.17 

58.64 

51.43 

58.42 

51.68 

58.19 

51.94 

78 

79 

59.62 

51.83 

59.40 

52.09 

59.17 

52.35 

!58.94 

52.60 

79 

80 

60.38 

52.48 

60.15 

52.75 

59.92 

53.01 

59.68 

53.27 

80 

81 

61.13 

53.14 

60.90 

53.41 

60.67 

53.67 

60.43 

53.94 

81 

82 

61.89 

53.80 

61.65 

54.07 

61.4J 

54.33 

61.18 

54.60 

82 

83 

62.64 

54.45 

62.40 

54.73 

62.16 

55.00 

61.92 

55.27 

83 

84 

63.40 

55.11 

6.3.15 

55.38 

62.91 

55.66 

62.67 

55.93 

84 

85 

64.15 

55.76 

63.91 

56.04 

63.66 

56.32 

63.41 

56.60 

85 

86 

64.90 

56.42 

64.66 

56.70 

64.41 

56.99 

64.16 

57.27 

86 

87 

65.66 

57.08 

65.41 

57.36 

65.16 

57.65 

64.91 

57.93 

87 

88 

66.41 

57.73 

66.16 

58.02 

65.91 

58.31 

|65.65 

58.60 

88 

89 

67.17 

58.39 

66.91 

58.68 

66.66 

58.97 

i66.40 

59.26 

89 

90 

67.92 

59.05 

67.67 

59.34 

67.41 

59.64 

67. 15 

59.93 

90 

91 

68.68 

59.70 

68.42 

60.00 

68 . 15 

60.30 

67.89 

60.60 

91 

92 

69.43 

60.36 

69.17 

60.66 

68.90 

60.96 

68.64 

61.26 

92 

93 

70.19 

61.01 

69.92 

61.32 

69.65 

61.62 

69.38 

61.93 

93 

94 

70.94 

61.67 

70.67 

61.98 

70.40 

62.29 

70.13 

62.59 

94 

95 

71.70 

62.33 

71.43 

62.64 

71.15 

62.95 

70.88 

63.26 

95 

96 

72.45 

62.98 

72.18 

63.30 

71.90 

63.61 

71.62 

63.92 

96 

97 

73.21 

63.64 

72.93 

63.96 

72.65 

64.27 

72.37 

64.59 

97 

93 

73.96 

64.29 

73.68 

64.62 

73.40 

64.94 

73.11 

65.26 

98 

99 i 

74.72 

64.95 

74.43 

65.28 

74.15 

65.60 

73.86 

65.92 

99 

100 

75.47 

65.61 

75.18 

65.93 

74.90 

66.26 

74.61 

66.59 

100 

• 

o 

o 

a 

Dep> ] 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

c 

u 

s 

ei 
—* 

CO 

•>« 

D 

49 Deg. 

48| Deg. 

48 ^ Deg. 

48| Deg. 

03 

»i 

ac 

P 

tlMMh 






































































































86 


TKAVERSE TABLE. 


c 
»— • 

Ul 

42 Deg. 

42k Deg. 

42^ Deg. 

42k Deg 

O 

75* 

r** 

P 

3 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

O 

o 

1 

0.74 

0.67 

0.74 

0.67 

0.74 

0.68 

0.73 

0.68 

1 

2 

1.49 

1 .34 

1.48 

1.34 

1.47 

1.35 

1.47 

1.36 

2 

a 

2.23 

2.01 

2.22 

2.02 

2.21 

2.03 

2.20 

2.04 

3 

4 

2.97 

2.68 

2.96 

2.69 

2.95 

2.70 

2.94 

2.72 

-1 

5 1 

3.72 

3.35 

3.70 

3.36 

3.69 

3.38 

3.67 

3.39 

5 

6 

4.46 

4.01 

4.44 

4.03 

4.42 

4.05 

4.41 

4.07 

6 

7 

5.20 

4.68 

5.18 

4.71 

5.16 

4.73 

5.14 

4.75 

7 

6 

5.95 

5.35 

5.92 

5.38 

5.90 

5.40 

5.87 

5.43 

8 

9 

6.69 

6.02 

6.66 

6.05 

6.64 

6.08 

6.61 

6.11 

9 

10 

7.43 

6.69 

7.40 

6.72 

7.37 

6.76 

7.34 

6.79 

10 

11 

8.17 

7.36 

8.14 

7.40 

8.11 

7.43 

8.08 

7.47 

11 

12 

8.92 

8.03 

8.88 

8 -. 07 

8.85 

8.11 

8.81 

8.15 

12 

13 

9.66 

8.70 

9.62 

8.74 

9.58 

8.78 

9.55 

8.82 

13 

14 

10.40 

9.37 

10.36 

9.41 

10.32 

9.46 

10.28 

9.50 

14 

15 

11.15 

10.04 

11.10 

10.09 

11.06 

10.13 

11.01 

10.18 

15 

16 

11.89 

10.71 

11.84 

10.76 

11.80 

10.81 

11.75 

10.86 

16 

17 

12.63 

11.38 

12.58 

11.43 

12.53 

11.48 

12.48 

11.54 

17 

18 

13.38 

12.04 

13.32 

12.10 

13.27 

12.16 

13.22 

12.22 

IS 

19 

14.12 

12.71 

14.06 

12.77 

14.01 

12.84 

13.95 

12.90 

19 

20 

14.86 

13.38 

14.80 

13.45 

14.75 

13.51 

14.69 

13.58 

20 

21 

15.61 

14.05 

15.54 

14.12 

15.48 

14.19 

15.42 ! 

14.25 

21 

22 

16.35 

14.72 

16.28 

14.79 

16.22 

14.86 

16.16 

14.93 

22 

23 

17.09 

15.39 

17.02 

15.46 

16.96 

15.54 

16.89 

15.61 

23 

24 

17.84 

16.06 

17.77 

16.14 

17.69 

16.21 

17.62 

16.29 

24 

25 

18.58 

16.73 

18.51 

16.81 

18.43 

16.89 

18.36 

16.97 

25 

26 

19.32 

17.40 

19.25 

17.48 

19.17 

17.57 

19.09 

17.65 

26 

27 

20.06 

18.07 

19.99 

18.15 

19.91 

18.24 

19. S3 

18.33 

27 

2S 

20.81 

18.74 

20.73 

18.83 

20.64 

18.92 

20.56 

19.01 

28 

29 

21.55 

19.40 

21.47 

19.50 

21.39 

19.59 

21.30 

19.69 

29 

30 

22.29 

20.07 

22.21 

20.17 

22.12 

20.27 

22.03 

20.36 

30 

31 

23.04 

20.74 

22.95 

20.84 

22.86 

20.94 

22.76 

21.04 

31 

32 

23.78 

21.41 

23.69 

21.52 

23.59 

21.62 

23.50 

21.72 

32 

33 

24.52 

22.08 

24.43 

22.19 

24.33 

22.29 

24.23 

22.40 

33 

34 

25.27 

22.75 

25.17 

22.86 

25.07 

22.97 

24.97 

23.08 

34 

35 

26.01 

23.42 

25.51 

23.53 

25.80 

23.65 

25.70 

23.76 

35 

36 

26.75 

24.09 

26.65 

24.21 

26.54 

24.32 

26.44 

24.44 

36 

37 

27 50 

24.76 

27.39 

24. SS 

27.28 

25.00 

27.17 

25.12 

37 

38 

28.24 

25.43 

28.13 

25.55 

28.02 

25.67 

27.90 

25.79 

38 

39 

28.98 

26.10 

28.87 

26.22 

28.75 

26.35 

28.64 

26.47 

39 

40 

29.73 

26.77 

29.61 

26.89 

29.49 

27.02 

29.37 

27.15 

40 

41 

39.47 

27.43 

30.35 

27.57 

30.23 

27.70 

30.11 

27.83 

41 

42 

31.21 

28.10 

31.09 

28.24 

30.97 

28.37 

30.84 

28.51 

42 

43 

31.96 

28.77 

31.83 

28.91 

31.70 

29.05 

31.58 

29.19 

43 

44 

32.70 

29.44 

32.57 

29.5S 

32.44 

29.73 

32.31 

29.87 

11 

45 

33.44 

30.11 

33.31 

30.26 

33.18 

30.40 

j 33.04 

30.55 

15 

46 

I 34.18 

30.78 

34.05 

30.93 

33.91 

31.08 

33.78 

31 .22 

46 

47 

34.93 

31.45 

34.79 

31.60 

34.65 

31.75 

1 34.51 

31 .90 

47 

48 

35.67 

32.12 

35.53 

32.27 

35.39 

32.43 

35.25 

32.58 

48 

49 

36.41 

32.79 

36.27 

32.95 

36.13 

33.10 

35.98 

33.26 

49 

50 

37.16 

33.46 

37.01 

33.62 

36.86 

33.78 

36.72 

33.9-1 

50 

6 

Q 

c 

eg 

5 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

c 

48 Deg. 

47| Deg. 

47£ Deg. 

47^ Deg. 

eg 

5 











































































































TRAVERSE TABLE- 


87 


o 
1— • 

P 

3 

O 

<3 

• 

i 

42 Deg. 

42} Deg. 

42} Deg. 

42} Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

r,i 

37.90 

34.13 

37.75 

34.29 

37.60 

34.46 

37.45 

34.62 

51 

53 

38.64 

34.79 

38.49 

34.96 

38.34 

35.13 

38.18 

35.30 

52 

53 

39.39 

35.46 

39.23 

35.64 

39.08 

35.81 

38.92 

35.98 

53 

54 

40.13 

36.13 

39.97 

38.31 

39.81 

36.48 

39.65 

36.66 

54 

55 

40.87 

36.80 

40.71 

36.98 

40 55 

37.16 

40.39 

37.33 

55 

56 

41.62 

37.47 

41.45 

37.65 

41.29 

37.83 

41.12 

38.01 

56 

67 

42.36* 

38.14 

42.19 

38.32 

42.02 

38.51 

41.86 

38.69 

57 

58 

43.10 

38.81 

42.93 

39.00 

42.76 

39.18 

42.59 

39.37 

58 

59 

43.85 

39.48 

43.67 

39.67 

43.50 

39.86 

43.32 

40.05 

59 

60 

44.59 

40.15 

44.41 

40.34 

44.24 

40.54! 

44.06 

40.73 

60 

61 

45.33 

40.82 

45.15 

41.01 

44.97 

41.21 

44.79 

41.41 

61 

62 

46.07 

41.49 

45.89 

41.69 

45.71 

41.89 

45.53 

42.09 

62 

63 

46.82 

42.16 

46.63 

42.36 

46.45 

42.56 

46.26 

42.76 

63 

64 

47.56 

42.82 

47.37 

43.03 

47.19 

43.24 

47.00 

43.44 

64 

65 

48.30 

43.49 

48.11 

43.70 

47.92 

43.91 

47.73 

44.12 

65 

66 

49.05 

44.16 

48.85 

44.38 

48.66 

44.59 

48.47 

44.80 

66 

67 

49.79 

44.83 

49.59 

45.05 

49.40 

45.26 

49.20 

45.48 

67 

68 

50.53 

45.50 

50.33 

45.72 

50.13 

45.94 

49.93 

46.16 

68 

69 

51.28 

46.17 

51.07 

46.39 

50.87 

46.62 

50.67 

46.84 

69 

70 

52.02 

46.84 

51.82 

47.07 

51.61 

47.29 

51.40 

47.52 

70 

71 

52.76 

47.51 

52.56 

47.74 

52.35 

47.97 

52.14 

48.19 

71 

72 

53.51 

48.18 

53.30 

48.41 

53.08 

48.64 

52.87 

48.87 

72 

73 

54.25 

48.85 

54.04 

49.08 

53.82 

49.32 

53.61 

49.55 

73 

74 

54.99 

49.52 

54.78 

49.76 

54.56 

49.99 

54.34 

50.23 

74 

75 

55.74 

50.18 

55.52 

50.43 

55.30 

50.67 

155.07 

50.91 

75 

76 

56.48 

50.85 

56.26 

51.10 

56.03 

51.34 

i55.81 

51.59 

76 

77 

57.23 

51.52 

57.00 

51.77 

56.77 

52.02 

!56.54 

52.27 

77 

78 

57.97 

52.19 

57.74 

52.44 

57.51 

52.70 

57.28 

52.95 

78 

79 

58.71 

52.86 

58.48 

53.12 

58.24 

53.37 

58.01 

53.63 

79 

80 

59.45 

53.53 

59.22 

53.79 

58.98 

54.05 

I 58.75 

54.30 

80 

81 

60.19 

54.20 

59.96 

54.46 

59.72 

54.72 

59.48 

54.98 

81 

82 

60.94 

54.87 

60.70 

55.13 

60.46 

55.40 

j 60.21 

55.66 

82 

83 

61.68 

55.54 

61.44 

55.81 

61.19 

56.07 

60.95 

56.34 

83 

84 

62.42 

56.21 

62.18 

56.48 

61.93 

56.75 

61.68 

57.02 

84 

85 

63.17 

56.88 

62.92 

57.15 

62.67 

57.43 

|62.42 

57.70 

85 

86 

63.91 

57.55 

63.66 

57.82 

63.41 

58.10 

63.15 

58.38 

86 

87 

34.65 

58.21 

64.40 

58.50 

64.14 

58.78 

i63.89 

59.06 

87 

88 

65.40 

58.88 

65.14 

59.17 

64.88 

59.45 

64.62 

59.73 

88 

89 

66.14 

59.55 

65.88 

59.84 

65.62 

60.13 

65.35 

60.41 

89 

90 

66.88 

60.22 

66.62 

60.51 

66.35 

60.80 

66.09 

61.09 

90 

91 

67.63 

60.89 

67.36 

61.19 

67.09 

61.48 

66.82 

61.77 

91 

92 

68.37 

61.56 

6 S.10 

61.86 

67.83 

62.15 

67.56 

62.45 

92 

93 

69.11 

62.23 

63.84 

62.53 

68.57 

62.83 

68.29 

63.13 

93 

94 

69.86 

62.90 

69.58 

63.20 

69.30 

63.51 

i69.03 

63.81 

94 

95 

70.60 

63.57 

70.32 

63.87 

70.04 

64.18 

69.76 

64.49 

95 

96 

71.34 

64.24 

71.06 

64.55 

70.78 

64.86 

70.49 

65.16 

96 

97 

72.08 

64.91 

71.80 

65.22 

71.52 

65.53 

71.23 

65.84 

97 

98 

72.83 

65.57 

72.54 

65.89 

72.25 

66.21 

71.96 

66 52 

98 

99 

73.57 

66.24 

73.28 

66.56 

72. 99 

66.88 

72.70 

67.20 

99 

1.00 

74.31 

66.91 

74.02 

67.24 

73.73 

67.56 

73.43 

67.88 

100 

« 

a 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

o 

c 

c n 

s 

| 

48 Deg. 

47f Deg. J 

47J Deg. 

47} Deg. 

D 

Q J 











































































































88 


TRAVERSE TABLE. 


Distance. 

43 Deg. 

43$ Deg. 

43$ Deg. 

431 Deg. 

e 

H • 

CO 

c+ 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

n 

? 

1 

0.73 

0.68 

0.73 

0.69 

0.73 

0.69 

0.72 

0.69 

1 

o 

1.46 

1 .36 

1.46 

1.37 

1.45 

1.38 

1.44 

1.38 

2 

3 

2.19 

2.05 

2.19 

2.06 

2.18 

2.07 

2.17 

2.07 

3 

4 

2.93 

2.73 

2.91 

2.74 

2.90 

2.75 

2.89 

2 77 

4 

5 

3.66 

3.41 

3.64 

3.43 

3.63 

3.44 

3.61 

3 46 

5 

6 

4.39 

4.09 

4.37 

4.11 

4.35 

4.13 

4.33 

4.15 

S 

7 

5.12 

4.77 

5.10 

4. SO 

5.08 

4.82 

5.06 

4.84 

7 

8 

5.85 

5.46 

5.83 

5.48 

5.80 

5.51 

5.78 

5.53 

8 

9 

6.58 

6.14 

6.56 

6.17 

6 .53 

6.20 

6.50 

6.22 

9 

10 

7.31 

6.82 

7.28 

6.85 

7.25 

6.88 

7.22 

0 92 

10 

11 

8.04 

7.50 

8.01 

7.54 

7.98 

7.57 

7.95 

7.61 

11 

12 

8.78 

8.18 

8.74 

8.22 

8.70 

8.26 

8.67 

8.30 

12 

13 

9.51 

8.87 

9.47 

8.91 

9.43 

8.95 

9.39 

8.99 

13 

14 

10.24 

9.55 

10.20 

9.59 

10.16 

9.64 

10.11 

9.08 

14 

15 

10.97 

10.23 

10.93 

10.28 

10.88 

10.33 

10.84 

10.37 

15 

16 

11.70 

10.91 

11.65 

10.96 

11.61 

11.01 

11.56 

11.00 

16 

17 

12.43 

11.59 

12.38 

11.65 

12.33 

11.70 

12.28 

11.76 

17 

18 

13.16 

12.28 

13.11 

12.33 

13.06 

12.39 

13.00 

12.45 

18 

19 

13.90 

12.96 

13.S4 

13.02 

13.78 

13.08 

13.72 

13.14 

19 

20 

14.63 

13.64 

14.57 

13.70 

14.51 

J3.77 

14.45 

13.83 

20 

21 

15.36 

14.32 

15.30 

14.39 

15.23 

14.46 

15.17 

14.52 

21 

22 

16.09 

15.00 

13.02 

15.07 

15.96 

15.14 

15.89 

15.21 

22 

23 

16.82 

15.69 

16.75 

15.76 

10.68 

15.83 

16.61 

15.90 

23 

24 

17.55 

16.37 

17.48 

16.44 

17.41 

16.52 

17.34 

16.60 

24 

25 

18.28 

17.05 

18.21 

17.13 

18.13 

17.21 

18.06 

17.29 

25 

26 

19.02 

17.73 

18.94 

17.81 

18.86 

17.90 

18.78 

17.98 

26 

27 

19.75 

18.41 

19.67 

18 50 

19.53 

18.59 

19.50 

18.67 

27 

28 

20.43 

19.10 

20.39 

19.19 

20.31 

19.27 

20.23 

19.36 

28 

29 

21.21 

19.78 

21.12 

19.87 

21.04 

19.96 

20.95 

20.05 

29 

30 

21.94 

20.46 

21.85 

20.56 

21.76 

20.65 

21.67 

20.75 

30 

51 

22.67 

21.14 

22.58 

21.24 

22.49 

21.34 

22.39 

21.44 

31 

32 

23.40 

21.82 

23 31 

21.93 

23.21 

22.03 

23.12 

22.13 

32 

33 

24.13 

22.51 

24.04 

22.61 

23.94 

22.72 

23.84 

22.82 

33 

34 

24.87 

23.19 

24.76 

23.30 

24.66 

23.40 

24.56 

23.51 

34 

35 

25.60 

23.87 

25.49 

23.98 

25.39 

24.09 

25.28 

24.20 

35 

30 

26.33 

24.55 

26.22 

24.67 

26.11 

24.78 

26.01 

24.89 

36 

37 

27.06 

25.23 

26.95 

25.35 

26.84 

25.47 

26.73 

25.59 

37 

33 

27.79 

25.92 

27.68 

26.04 

27.56 

26.16 

27.45 

26.28 

38 

39 

28.52 

26.60 

28.41 

26.72 

28.29 

26.85 

28.17 

26.97 

39 

40 

29.25 

27.28 

29.13 

27.41 

29.01 

27.53 

28.89 

27.66 

40 

41 

29.99 

27.96 

29.86 

28.09 

29.74 

28.22 

29.62 

28.35 

41 

42 

30.72 

28.64 

30.59 

28.78 

30.47 

28.91 

30.34 

29.04 

42 

43 

31.45 

29.33 

31.32 

29.46 

31.19 

29.60 

31.06 

29.74 

43 

44 

32.18 

30.01 

32.05 

50.15 

31.92 

30.29 

31.78 

30.43 

44 

45 

32.91 

30.69 

32.78 

30.83 

32.64 

30.98 

32.51 

31.12 

45 

46 

33.64 

31.37 

33.51 

31.52 

33.37 

31.66 

33.23 

31.81 

| 46 

47 

34.37 

32.05 

34.23 

32.20 

34.09 

32.35 

33.95 

32.50 

47 

48 

35.10 

32.74 

34.96 

32.89 

34.82 

33.04 

34.67 

33.19 

! 48 ' 

49 

35.84 

33.42 

35.69 

33.57 

35.54 

33.73 

35.40 

33 88 

49 

50 

36.57 

34.10 

36.42 

34.26 

36.27 

34.42 

36.12 

34.58 

50 

6 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dap. 

L>* 

6 

o 

a 

a 

-*-» 

CO 

• M 

Q 

47 Deg. 

46| Deg. 

46$ Deg. 

46$ Deg 

.1 










uJ 

































































































TRAVERSE TABLE. 


89 


c 

ST 

<-*■ 

p 

43 Deg. 

43} Deg. 

431 

Deg. 

43| Deg. 

a 

OR 

r-* 

P 

s 

o 

ce 

Lat. 

Dep. 

Lat. | 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Zj 

O 

9 

61 

37.30 

34.78 

37.15 

34.94 

36.99 

35.11 

36.84 

35.27 

51 

62 

38.03 

35.46 

37.88 

35.63 

37.72 

35.79 

37.56 

35.96 

52 

53 

38.76 

36.15 

38.60 

36.31 

38.44 

36.48 

38.29 

36.65 

53 

61 

39.49 

36.83 

39.33 

37.00 

39.17 

37.17 

39.01 

37.34 

54 

65 

40.22 

37.51 

40.06 

37.69 

39.90 

37.86 

39.73 

38.03 

55 

66 

40.96 

38.19 

40.79 

38.37 

40.62 

38.55 

40.45 

38.72 

56 

67 

41.69 

38.87 

41.52 

39.06 

41.35 

39.24 

41.17 

39.42 

57 

68 

42.42 

39.56 

42.25 

39.74 

42.07 

39.92 

41.90 

40.11 

58 

59 

43.15 

40.24 

42.97 

40.43 

42.80 

40.61 

42.62 

40.80 

59 

60 

43.88 

40.92 

43.70 

41.11 

43.52 

41.30 

43.34 

41.49 

60 

61 

44.61 

41.60 

44.43 

41.80 

44.25 

41.99 

44.06 

42.18 

61 

62 

45.34 

42.28 

45.16 

42.48 

44.97 

42.68 

44.79 

42.87 

62 

63 

46.08 

42.97 

45.89 

43.17 

45.70 

43.37 

45.51 

43.57 

63 

64 

46.81 

43.65 

40.62 

43.85 

46.42 

44.05 

46.23 

44.26 

64 

65 

47.54 

44.33 

47.34 

44.54 

47.15 

44.74 

46.95 

44.95 

65 

66 

48.27 

45.01 

48.07 

45.22 

47.87 

45.43 

47.68 

45.64 

66 

67 

49.00 

45.69 

48.80 

45.91 

48.60 

46.12 

48.40 

46.33 

67 

68 

49.73 

46.38 

49.53 

46.59 

49.33 

46.81 

49.12 

47.02 

68 

69 

50.46 

47.06 

50.26 

47.28 

50.05 

47.50 

49.84 

47.71 

69 

70 

51.19 

47.74 

50.99 

47.96 

50.78 

48.18 

50.57 

48.41 

70 

71 

51.93 

48.42 

51.71 

4S.65 

51.50 

48.87 

51.29 

49.10 

71 

72 

52.66 

49.10 

52.44 

49.33 

52.23 

49.56 

52.01 

49.79 

72 

73 

53.39 

49.79 

53.17 

50.02 

52.95" 

'50.25 

52.73 

50.48 

73 

74 

54.12 

50.47 

53.90 

50.70 

53.68 

50.94 

53.45 

51.17 

74 

75 

54.85 

51.15 

54.63 

51.39 

54.40 

51.63 

54.18 

51.86 

75 

76 

55.58 

51.83 

55.36 

52.07 

55.13 

52.31 

54.90 

52.55 

76 

77 

56.31 

52.51 

56.08 

52.76 

55.85 

53.00 

55.62 

53.25 

77 

78 

57.05 

53.20 

56.81 

53.44 

56.58 

53.69 

56.34 

53.94 

78 

79 

57.78 

53.88 

57.54 

54.13 

57.30 

54.38 

57.07 

54.63 

79 

80 

58.51 

54.56 

58.27 

54.81 

58.03 

55.07 

57.79 

55.32 

JO 

81 

59.24 

55.24 

59.00 

55.50 

58.76 

55.76 

58.51 

56.01 


82 

59.97 

55.92 

59.73 

56.18 

59.48 

56.45 

59.23 

56.70 

82 

83 

60.70 

56.61 

60.45 

56.87 

60.21 

57.13 

59.96 

57.40 

83 

84 

61.43 

57.29 

61.18 

57.56 

60.93 

57.82 

60.68 

58.09 

84 

85 

62.17 

57.97 

61.91 

58.24 

61.66 

58.51 

61.40 

58.78 

85 

86 

62.90 

58.65 

62.64 

58.93 

62.38 

59.20 

62.12 

59.47 

86 

87 

63.63 

59.33 

63.37 

59.61 

63.11 

59.89 

62.85 

60.16 

87 

88 

64.36 

60.02 

64.10 

60.30 

63.83 

60.58 

63.57 

60.85 

88 

89 

05.09 

60.70 

64.82 

60.98 

64.56 

61.26 

64.29 

61.54 

89 

90 

65.82 

61 .38 

65.55 

61.67 

65.28 

61.95 

65.01 

62.24 

90 

91 

66.55 

62.06 

66.28 

62.35 

66.01 

62.64 

65.74 

62.93 

91 

92 

67.28 

62.74 

67.01 

63.04 

66.73 

63.33 

66.46 

63.62 

92; 

93 

68.02 

63.4? 

67.74 

63.72 

67.46 

64.02 

67.18 

64.31 

93 

94- 

68.75 

64.11 

68.47 

64.41 

68.19 

64.71 

67.90 

65.00 

1 94 

So 

69.48 

i 64.79 

69.20 

65.09 

68.91 

65.39 

68.62 

65.69 

95 

96 

70.21 

65.47 

69.92 

65.78 

69.64 

66.08 

69.35 

66 .39 

96 

97 

70.94 

66.15 

70.65 

60.46 

70.36 

66.77 

70.07 

67.08 

97 

98 

71.67 

66.84 

71.37 

67.15 

71.09 

67.46 

70.79 

67.77 

98 

99 

72.40 

67.52 

72.11 

67.83 

71.81 

68.15 

71.51 

68.46 

99 | 

100 

73.14 

68.20 

72.84 

68.52 

72.54 

68.84 

72.24 

69.15 

100 

6 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

o 

c 

d 

•*-> 

CG 

I>p4 

Q 

4'< Deg. 

461 Deg. 

461 

Deg. 

46} Deg. 

0Q 

Q 




I 
















































































































90 


TKAVERSE TABLE 


o 

35' 

<-► 

P 

5 

6 

44 Deg 


44\ Deg. 

44 i Deg. 

44J Deg. 

45 Deg. 

O 

5T 

P 

3 

O 

O 

Lai. 

Dep. 


Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

0 . 

72 

0 . 

69 

0 . 

72 

0.70 

0.71 

0.70 

0 . 

71 

0 . 

71 

0 . 

71 

0 . 

71 

1 

2 

1 . 

44 

1 . 

39 

1 . 

43 

1.40 

1.43 

1.40 

1. 

42 

1 . 

41 

1. 

41 

1 . 

41 

2 

3 

2 . 

16 

2 . 

08 

2 . 

15 

2.09 

2.14 

2.10 

2 . 

13 

2 . 

11 

2 . 

12 

2 . 

12 

3 

4 

2 . 

88 

2 . 

78 

2 . 

87 

2.79 

2.85 

2.80 

2 . 

84 

2 . 

82 

2 . 

83 

o 

83 

4 

ft 

3 

60 

3. 

47 

3. 

58 

3.49 

3.57 

3 50 

3. 

55 

3. 

52 

3. 

54 

3. 

54 

0 

6 

4 

32 

4. 

17 

4. 

30 

4.19 

4.28 

4.21 

4. 

26 

4. 

22 

4. 

24 

4. 

24 

e 

7 

5 

04 

4. 

86 

5. 

01 

4.88 

4.99 

4.91 

4. 

97 

4. 

93 

4. 

95 

4. 

95 

i 

8 

5 

75 

5. 

56 

5. 

73 

5.58 

5.71 

5.61 

5. 

68 

5. 

63 

5. 

66 

5 . 

66 

8 

9 

6 

47 

6 . 

25 

6 . 

45 

6.28 

6.42 

6.31 

6 . 

39 

6 . 

34 

6 . 

36 

6 . 

36 

9 

10 

7 

19 

6 . 

95 

7. 

16 

6.98 

7.13 

7.01 

7. 

10 

7. 

04 

7. 

07 

7. 

07 

10 

11 

7 

91 

7. 

64 

7. 

88 

7.68 

7.85 

7.71 

7. 

81 

7. 

74 

7. 

78 

7. 

78 

11 

12 

8 

63 

8 . 

34 

8 . 

60 

8.37 

8.56 

8.41 

8 . 

52 

8 . 

45 

8 . 

49 

8 . 

49 

12 

13 

9. 

35 

9. 

03 

9. 

31 

9.07 

9.27 

9.11 

9. 

23 

9. 

15 

9. 

19 

9. 

19 

13 

14 

10 

07 

9. 

73 

10 . 

03 

9.77 

9.99 

9.81 

9. 

94 

9. 

86 

9. 

90 

9. 

90 

14 

15 

10 

79 

10 . 

42 

10 . 

74 

10.47 

10.70 

10.51 

10 . 

65 

10 . 

56 

10 . 

61 

10 . 

61 

15 

16 

11 

51 

11 . 

11 

11 . 

46 

11.16 

11.41 

11.21 

11 . 

36 

11 . 

26 

11 . 

31 

11 . 

31 

16 

17 

12 

23 

11 . 

81 

12 . 

18 

11.86 

12.13 

11.92 

12 . 

07 

11 . 

97 

12 . 

02 

12 . 

02 

17 

18 

12 

95 

12 . 

50 

12 . 

89 

12.56 

12.84 

12.62 

12 . 

78 

12 . 

67 

12 . 

73 

12 . 

73 

18 

19 

13 

67 

13. 

20 

13. 

61 

13.26 

13.55 

13.32! 

13. 

49 

13. 

38 

13. 

43 

13. 

43 

19 

20 

14 

39 

13. 

89 

14. 

33 

13.96 

14.26 

14.02 

14. 

20 

14. 

08 

14. 

14 

14. 

14 

20 

21 

15 

11 

14. 

59 

15. 

04 

14.65 

14.98 

14.72! 

14. 

91 

14. 

78 

14. 

85 

14. 

85 

21 

22 

15 

83 

15. 

28 

15. 

76 

15.35 

15.69 

15.42! 

15. 

62 

15. 

49 

15. 

56 

15. 

56 

22 

23 

16 

54 

15. 

98 

16. 

47 

16.05 

16.40 

16.12! 

16. 

33 

16. 

19 

16. 

26 

16. 

26 

23 

24 

17 

26 

16. 

67 

17. 

19 

16.75] 

17.12 

16.82 1 

17. 

04 

16. 

90 

16. 

97 

16. 

97 

24 

25 

17 

98 

17. 

37 

17. 

91 

17.44 

17.83 

17.52 

17. 

75 

17. 

60 

17. 

68 

17. 

68 

25 

26 

18 

70 

18. 

06 

18. 

62 

18.14! 

18.54 

18.22 

18. 

46 

18. 

30 

18. 

38 

IS. 

38 

26 

27 

19 

42 

18. 

76 

19. 

34 

18.84-1 

19.26 

18.92 

19. 

17 

19. 

01 

19. 

09 

19. 

09 

27, 

28 

20 

14 

19. 

45 

20 . 

06 

19.54 

19.97 

19.63* 

19. 

89 

19. 

71 

19. 

80 

19. 

80 

28 

29 

20 

86 20 . 

15 

20 . 

77 

20.24 

20.68 

20.33 

20 . 

60 

20 . 

42 

20 . 

51 

20 . 

51 

29 

30 

21 

58 

20 . 

84 

21 . 

49 

20.93 

21.40 

21.03 

21 

31 

21 . 

12 

21 . 

21 

21 . 

21 

30 

31 

22 

30 

21 . 

53 

22 . 

21 

21.63 

22.11 

21.73 

22 

02 

21 . 

82 

21 . 

92 21 . 

92 

31 

32 23 

02 

22 . 

23 

22 . 

92 

22.33 

22.82 

22.43 

22 . 

73 

22 . 

53 

22 . 

63 22 . 

63 

32 

33,23 

74 

22 . 

92 

23. 

64 

23.03 

23.54 

23.13 

23. 

44 

23. 

23 

23. 

33 23. 

33 

33 

34124 

46 

23. 

62 

24. 

35 

23.72 

24.25 

23.83 

24. 

15 

23. 

94 

24 

04'24. 

04 

34 

35 

25 

18 

24. 

31 

25. 

07 

24.42 

24.96 

24.53 

24. 

86 

24. 

64 

24 

75 

24 

75 35 

36 

25 

90 

25. 

01 

25. 

79 

25.12 

25.68 

25.23 

25. 

57 

25 

34 

25 

46 

25 

46 36 

37 26 

62 

25. 

70 

26. 

50 

25.82 

26.39 

25.93 

26 

28 

26 

05 

26 

.16 

26 

16 

37 

38 

27 

33 

26. 

40 

27. 

22 

26.52 

27.10 

26.63 

26 

99 

26 

75 

26 

.87 

26 

87 

38 

39 

28 

05 

27. 

09 

27 

94 

27.21 

27.82 

27.34 

27 

70 

27 

46 

27 

.58 

27 

.58 

39 

40 

28 

77 

27. 

79 

28 

65 

27.91 

28.53 

28.04 

28 

.41 

28 

16 

28 

.28 

v28 

.28 

40 

41 

29 

.49 

28. 

48 

29 

37 

28.61 

29.24 

28.74 

29 

.12 

28 

.86 

28 

.99 

28 

.99 

41 

42 

30 

.21 

29. 

18 

30 

OS 

29.31 

29.96 

29.44 

29 

.83 

29 

.57 

29 

.70 

29 

.70 

42 

43 

30 

.93 

29. 

87 

30 

80 

30.00 

30.67 

30.14 

30 

.54 

30 

.27 

30 

.41 

30 

.41 

43 

44 

31 

.65 

30. 

56 

31 

.52 

30.70 

31.38 

30.84 

31 

.25 

30 

.98 

31 

.11 

31 

.11 

44 

45 

32 

.37 

31. 

26 

32 

23 

31.40 

32.10 

31.54 

31 

.96 

31 

.68 

31 

.82 

31 

.82 

45 

46 

33 

.09 

31. 

95 

32 

95 

32.10 

32.81 

32.24 

32 

67132 

.38 

32 

.53 

32 

.53 

40 

47 

33 

.81 

32. 

65 

33 

.67 

32.80 

33.52 

32.94 

33 

38 

33 

.09 

33 

.23 

33 

.23 

41 

48 

34 

.53 

33. 

34 

34 

.38 

33.49 

34.24 

33.64 

34 

09 

33 

.79 

33 

.94 

33 

.94148 

49 

35 

.25 

34. 

04 

35 

.10 

34.19 

34.95 

34.34 

34 

80 

34 

.50 

34 

.65 

34 

.65 49 

50 

35 

.97 

34. 

73 

35 

.82 

34.89 

35.66 

35.05 

35 

.51 

35 

.20 

35 

.36 

35 

.36 

50 

Distance.] 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

] Dep. 

Lat. 

a3 

V 

u 

d 

*-> 

OD 

5 

46 Deg. « 

45 J Deg. 

45^ Deg. 

45$ Deg. 

45 Deg. 











































































































































TRAVERSE TABT-E, 


y. 


« 

w 

t/i* 

p 

44 Deg. 

44} Deg. 

I 

44} Deg. 

44? Deg. 

i 

45 Deg. 

j 

i 

D 

O 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 1 

Dep. 

Lat. 

Dei). 

1 


51 

36.69 

35.43 

36.53 

35.59 

36.38 35.75 

36.22*35.90 

36.06 

36.06 

52 

37.41 

36.12 

37.25 

36.29 

37.09 36.45 

36.93 

36.6 1 

36 .77 

36.77 

53 

38.12 

36.82 

137.96 

36.98 

37.80 

37.15 

37.64 

37.31 137.48 

37.48 

54 

38.84 

37.51 

38.68 

37.68 

38.52 

37.85 

38.35 

38.02 

38.18 

38.18 

55 

39,56 

38.21 

39.40 

38.38 

39.23 

38.55 

39.06 

38.72 

38.89 

38.89. 

56 

40,28 

38.90 

40.11 

39.08 

39.94 

39.25 

39.77 

39.42 

39.60 

39.60 

57 

41.00 

39.60 

40.83 

39.77 

40.66 

39.95 

40.48 

40.13 

40.31 

40.31 

i 

58 

41.72 

40.29 

41.55 

40.47 

41.37 

40.65 

41.19 

40.83 

41.01 

41.01 


59 

42.44 

40.98 

42.26 

41.17 

42.08 

41.35 

41.90 

4 1 .54' 

41.72 

41.72 

, 

60 

43.16 

41.68 

42.98 

41.87 

42.79 

42.05 

42.61 

42.241 

42.43 

42.43 


61 

43.88 

42.37 

43.69 

42.57 

43.51 

42.76 

43.32 

42.941 

43713 

43.13 


62 

44.60 

43.07 

44.41 

43.26 

44.22 

43.46 

44.03 

43.65! 

43.84 

43.84 


63 

45.32 

43.76 

45.13 

43.96 

44.93 

44.16 

44.74 

44.35 

44.55 

44.55 


64 

46.04 

44.46 

45.84 

44.66 

45.65 

44.86 

45.45 

45.06 

45.25 45.25 


65 

46.76 

45.15 

46.56 

45.36 

48.36 

45.56 

46.16 

45.76 

45.96 

45.96 


66 

47,48 

45.85 

47.28 

46.05 

47.0? 

46.26 

46.87 

46.40 

46.67 

46.67 


67 

48.20 

46.54 

47.99 

46.75 

47.79 

46.96 

47.58 

47.171 

47.38 

47.38 


68 

48.92 

47.24 

48.71 

47.45 

48.50 

47.66 

48.29 

47.87'i 

48.08 

48.08 


69 

49.63 

47.93 

49.42 

48.15 

49.21 

48.36 

49.00 

48.58 

48.79 

48.79 


70 

50.35 

48.63 

50.14 

48.85 

49.93 

49.06 

49.71 

49.28 

49.50 

49.50 


71 

51.07149.32 

50.86 

49.54 

50.64 

49.76 

50.42 

49.98! 

50.20 

50.20 


72 

51.79 50.02 

51.57 

50.24 

51.35 

50.47 

51.13 

50.69 

50.91 

50.91 


73 

52.51 

50.71 

52.29 

50.94 

52.07 

51.17 

51.84 

51.39 

51.62 

51.62 


74 

53.23 51.40 

53.01 

51.64 

52.78 

51.87 

52.55 

52.10 

52.33 

52.33 


75 

53.95 52.10 

53.72 

52.33 

53.49 

52.57 

53.26 

52.80 

53.03 

53.03 


76 

54,67 

52.79 

54.44 

53.03 

54.21 

53.27 

53.97 

53.51 

53.74 53.74 


77 

55.39 

53.49 

55.16 

53.73 

54.92 

53.97154.08 

54.21 

54.45 

54.45 


78 

56.11 

54.18 

55.87 

54.43 

55.63 

54.67 

55.39 

54.91 

55.15l55.15 


79 

56.83 

54.88 

56.59 

55.13 

56.35 

55.37 

56.10 

55.62 

55 .86 i 55 .86 


80 

57.55 

55.57 

57.30 

55.82 

5? .06 

56.07 

56.81 

56.32 

56.57 56.57 


81 

58.27 

56.27 

58.02 

56.52 

57.77 

56.77 

57.52 

57.03 

57.28157.28 


82 

08 .99 

56.96 

58.74 

57.22 

58.49 

57.47 

'58.24 

57.73 

57.98 57.98 


83 

59.71 

57.66 

59.45 

57.92 

59.20 

58.18 

58.95158.43! 

58.69'5S. 69 


84 

60.42 

58.35 

60.17 

58.61 

59.91 

58.88 

59.66 59.14! 

59.40’ 59.40 


85 

61.l4j59.05 

60.89 

59.31 

60.63 

59.58 

60.37 59.84! 

60.10 60.10 


86 

61.86150,74 

61.60 

uU . 01 

61.34 

60.28 

61.0860.55 

60.81 

no .81 


87 

62.5S;60.44 

62.32 

60.71 

62.05 

60.98 

01.79 61.25. 

61.52 

61 .52 


88 

63.30 61.13 

63.03 

61.41 

62.77 

61 .68 

62.50 61.95. 

62.23 62.23 


89 

64.02 61.82 

63.75 

62.10 

63.48 

62.38 

63.21 

62.66 

62.93 62.93 


90 

64.74 62.52 

64.47 

62.80 

64.19 

63.08 

63.92 63.36 

63.64 63.64 


91 

65.46 63.21 

65.18 

63.50 

64.91 

63.78 

64.63|64.07 

64.35 64.35 


92 

66.18163.91 

65.90 

64.20 

65.62 

64.48 

65.34 

64.77 

65.05 

65.05 


93 

66.90 64.60 

66.62 

64.89 

66.33 

65.18 

06.05 

65.47 

65.76i65.76 


94 

67.62:65.30 

67.33 

65.59 

67.05 

65.89 

06.76 66.18 

66.47 

66.47 


95 

68.34165.99 

68.05 

66.29 

67.76 

06.59 

67.47 66.88 

67.18j67.18 


96 

69.06 66.69 

68.76 

66.99 

68.47 

67.29 

08.18 67.59 

67.88167.88 


97 

69.78 67.38 

69.48 

67.69 

69.19 

67.99 

68.89 68.29 

168.59 68.59 


38 

70.50 68.08 

70.20 

G8.38 

69.90 

68 69 

69.60 

68.99 

69.30 69.30 


99 

71.21 68.77 

70.91 

69.08 

70.61 

69.39 

70.31 

69.70 

70.00 70.00 


100 

71.93 69.47 

71.63 

69.78 

71.33 

70.09 

71.02 

70.40 

70.71 70.71 

1 

8 

c 

Dep. 

Lit, 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

| Lat. 

i 

cd 

/ 

S3 

S 1 

i 

46 Deg. 

45? Deg. 

45} Deg. 

45} Deg. 

45 Eeg. 

| 

| 


o 

X 

<-*■ 

P 

3 


51 

52 

53 


61 

62 

63 

64 

65 

66 
67 
38 
63 

19 

71 

72 

73 

74 

75 

76 

77 

78 

79 

80 


81 

82 

83 

84 

85 

86 

87 

88 

89 

90 

91 

92 

93 

94 

95 

96 
9? 

98 

99 


a 

s1 




































































































































92 


I 


A TABLE OF RHUMBS. 


SHOWING 

Tfiff DEGREES, MINUTES, AND SECONDS, THAT EVERY POINT AND QUAMffS 

POINT OF TIIE COMPASS MAKES WITH 
THE MERIDIAN. 


NORTH. 

|Pts. 

qr. 

o 


1 

0 

1 

2 



I 

2 

5 



0 

3 

8 

N by E. 

N. by W. 

I 

0 

11 



1 

1 

14 



1 

2 

16 



1 

3 

J 9 

N.N.E. 

N.N.W. 

o 

*4 

0 

22 



2 

1 

25 



2 

2 

28 



O 

3 

30 

N.E.byN. 

N.W. by N. 

3 

0 

33 



3 

1 

33 



3 

2 

30 



3 

3 

42 

N.E 

N.W. 

4 

0 

45 



4 

1 

47 



4 

O 

50 



4 

3 

53 

N.E.byE. 

N.W.by W. 

5 

0 

5G 



5 

1 

59 



5 

2 

61 



5 

3 

64 

E N.E, 

W.N W. 

6 

0 

67 



6 

1 

70 



G 

2 

73 

• 


6 

3 

75 

Kbv N 

W. by N. 

7 

0 

78 

I 


7 

1 

81 



7 

2 

84 

1 


7 

3 

87 

£%St. 

West. 

8 

0 

90 


/ 

// 

| Pts. 

qr 

SOUTH. 

48 

45 

|0 

1 



37 

30 

0 

2 



26 

15 

0 

3 



15 

0 

1 

0 

S. by E. 

S. by W. 

3 

45 

1 

1 



52 

30 

1 

2 



41 

15 

1 

3 


\ 

30 

0 

9 

A* 

0 

S.S.E. 

s.s.w. 

IS 

45 

2 

1 



• 7 

30 

2 

2 



53 

15 

2 

3 



45 

0 

3 

0 

S.E. by S. 

S.W. by S 

33 

45 

3 

1 



22 

30 

3 

2 



11 

15 

3 

3 



0 

0 

4 

0 

S.E. 

S.W. 

48 

45 

4 

1 



37 

30 

4 

2 



26 

15 

4 

3 



15 

0 

5 

0 

S.E. byE. 

S.W. by W 

3 

45 1 

5 

1 



52 

30 

5 

2 



41 

15 

5 

3 



30 

0 

6 

0 

E.S.E. 

W S.W. 

18 

45 

6 

1 



7 

30 

6 

2 



56 

15 

6 

3 



45 

0 

7 

0 

E. by S. 

W. by 3 

33 

45 

7 

1 



22 

30 

7 

2 



11 

15 

7 

3 



0 

o| 

8 

0 

East. | 

West, 


y 


































workman’s table, for correcting the middle latitude. 9.3 


kid. 

30 
















L&t. 

40 


50 


60 


70 


80 


90 


10O 

| 

no 

o 

o ' 

o / 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

c 

/ 

15 

0 02 

0 03 

0 

04 

0 

06 

0 

09 

0 

12 

0 

15 

0 

19 

0 

23 

j 10 

0 02 

0 03 

0 

04 

0 

06 

0 

09 

0 

12 

0 

15 

0 

18 

0 

22 

17 

0 02 

0 03 

0 

04 

0 

06 

0 

08 

0 

11 

0 

14 

0 

17 

0 

21 

18 

0 02 

0 03 

0 

04 

0 

06 

0 

08 

0 

11 

0 

14 

0 

17 

0 

20 

19 

0 02 

0 03 

0 

04 

0 

06 

0 

07 

0 

10 

0 

13 

0 

16 

0 

19 

20 

0 02 

0 03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

21 

0 02 

0 03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

22 

0 02 

0 03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

17 

23 

0 02 

0 03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

17 

24 

C 02 

0 03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

25 

C 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

20 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

27 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

08 

0 

11 

0 

14 

0 

16 

28 

(> 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

29 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

30 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

31 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

32 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

33 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

34 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

35 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

36 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

37 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

38 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

39 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

40 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

41 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

42 

0 02 

0 03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

43 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

44 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

45 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

46 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

47 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

48 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

1G 

49 

0 02 

0 03 

0 

04 

0 05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

17 

50 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

17 

51 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

17 

52 

0 02 

0 03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

53 

0 02 

0 03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

54 

0 02 

0 03 

0 

04 

0 

06 

0 

08 

0 

10 

0 

13 

0 

16 

0 

19 

55 

0 02 

0 03 

0 

04 

0 

06 

0 

08 

0 

10 

0 

13 

0 

16 

0 

19 

56 

0 02 

0 03 

0 

04 

0 

06 

0 

08 

0 

10 

0 

13 

0 

16 

0 

20 

57 

0 02 

0 03 

0 

04 

0 

06 

0 

08 

0 

11 

0 

14 

0 

17 

0 

20 

58 

0 02 

0 03 

0 

04 

0 

06 

0 

09 

0 

11 

0 

14 

0 

17 

0 

21 

59 

0 02 

0 03 

0 

04 

0 

06 

0 

09 

0 

12 

0 

15 

0 

18 

0 

22 

60 

0 02 

0 03 

0 

04 

0 

06 

0 

09 

0 

12 

0 

15 

0 

19 

0 

23 

61 

0 02 

0 03 

0 

05 

0 

07 

0 

09 

0 

12 

0 

15 

0 

19 

0 

23 

62 

0 02 

0 03 

0 

05 

0 

07 

0 

09 

0 

12 

0 

16 

0 

20 

0 

24 

63 

0 02 

0 04 

0 

05 

0 

07 

0 

09 

0 

13 

0 

16 

0 

20 

0 

24 

64 

0 02 

0 04 

0 

06 

0 

08 

0 

09 

0 

13 

0 

17 

0 

21 

0 

25 

65 

0 02 

0 04 

0 

Ot 

0 

08 

0 

10 

0 

13 

0 

17 

0 

21 

0 

25 

66 

0 02 

0 04 

0 

06 

0 

08 

0 

10 

0 

14 

0 

18 

0 

22 

0 

26 

67 

0 02 

0 04 

0 

06 

0 

08 

0 

11 

0 

15 

0 

18 

0 

23 

0 

27 

68 

0 02 

0 04 

0 

06 

0 

08 

0 

11 

0 

15 

0 

19 

0 

24 

0 

28 

69 

0 02 

0 05 

0 

06 

0 

09 

0 

12 

0 

16 

0 

20 

0 

25 

0 

30 

70 

0 03 

0 05 

0 

06 

0 

09 

0 

13 

0 

17 

0 

21 

0 

26 

0 

31 

71 

0 04 

0 06 

0 

07 

0 

09 

0 

13 

0 

18 

0 

22 

0 

27 

0 

33 

72 

0 04 

0 06 

0 

08 

0 

10 

0 

14 

0 

19 

0 

23 1 

0 

29 

0 

35 


26 

































94 workman's table, for correcting the middle latitude. 


f Mil. 
Lat. 

> 

15 

120 

n / 

130 

O / 

o 

140 

/ 

o 

150 

/ 

o 

16< 

/ 

170 

o / 

180 

o / 

c 

L9° 

/ 

1 20 D 

1 o / 

0 

27 

0 

31 

0 

35 

0 

40 

0 

45 

0 51 

0 

58 

1 

(76 

1 

14 

16 

0 

26 

0 

30 

0 

34 

0 

38 

0 

43 

0 49 

0 

50 

1 

03 

1 

] 1 

17 

0 

25 

0 

28 

0 

32 

0 

37 

0 

42 

0 48 

0 

54 

1 

01 

l 

os : 

18 

0 

24 

0 

27 

0 

31 

0 

36 

0 

41 

0 46 

0 

52 

0 

58 

1 

06 j 

19 

0 

23 

0 

26 

0 

30 

0 

34 

0 

40 

0 45 

0 

50 

0 

56 

1 

03 

20 

0 

22 

0 

25 

0 

29 

0 

33 

0 

38 

0 43 

5 

48 

0 

54 

1 

oo ! 
5s ; 

21 

0 

21 

0 

25 

0 

29 

0 

33 

0 

37 

0 42 

(/ 

47 

i ° 

53 

G 

22 

0 

20 

0 

24 

0 

28 

0 

32 

0 

36 

0 41 

0 

4*? 

i 0 

51 

0 

56 j 

23 

0 

20 

0 

24 

0 

28 

0 

32 

0 

36 

0 40 

0 

45 

1 o 

50 

0 

55 t 

24 

0 

19 

0 

23 

0 

27 

0 

31 

0 

35 

0 39 

0 

44 

0 

48 

0 

53 } 

25 

0 

19 

0 

23 

0 

27 

0 

31 

0 

35 

0 39 

0 

43 

0 

47 

0 

52 {j 

26 

0 

19 

0 

22 

0 

26 

0 

30 

0 

34 

0 38 

0 

42 

0 

47 

0 

52 | 

27 

0 

19 

0 

22 

0 

26 

0 

30 

0 

33 

0 38 

0 

42 

0 

46 

0 

51 

28 

0 

18 

0 

21 

0 

25 

0 

29 

0 

33 

0 37 

0 

41 

0 

46 

0 

M 

29 

0 

18 

0 

21 

0 

25 

0 

29 

0 

32 

0 36 

0 41 

0 

45 

0 

50 

30 

0 

18 

0 

21 

0 

25 

0 

28 

0 

32 

0 36 

0 

41 

0 

45 

0 

50 

31 

0 

18 

0 

21 

0 

25 

0 

28 

0 

32 

0 36 

0 

41 

0 

45 

0 

50 

32 

0 

18 

0 

21 

0 

25 

0 

28 

0 

31 

0 36 

0 

41 

0 

45 

0 

50 

33 

0 

18 

0 

21 

0 

24 

0 

27 

0 

31 

0 35 

0 

40 

0 

44 

0 

49 

34 

0 

18 

0 

21 

0 

24 

0 

27 

0 

31 

0 35 

0 

40 

0 

44 

0 

49 

35 

0 

18 

0 

21 

0 

24 

0 

27 

0 

31 

0 35 

0 

40 

0 

44 

c 

49 

36 

0 

18 

0 

21 

0 

24 

0 

27 

0 

31 

0 35 

0 

40 

0 

44 

0 

49 

37 

0 

18 

0 

21 

0 

24 

0 

27 

0 

31 

0 35 

0 

40 

0 

44 

0 

49 

38 ' 

0 

18 

0 

21 

0 

24 

0 

27 

0 

31 

0 36 

0 

40 

0 

45 

0 

50 

39 

0 

18 

0 

21 

0 

25 

0 

28 

0 

32 

0 36 

0 

41 

0 

45 

0 

50 

40 

0 

18 

0 

22 

0 

25 

0 

28 

0 

32 

0 36 

0 

41 

0 

45 

0 

50 

41 

0 

18 

0 

22 

0 

25 

0 

28 

0 

32 

0 37 

0 

41 

0 

45 

0 

50 

42 

0 

18 

0 

22 

0 

26 

0 

29 

0 

33 

0 37 

0 

42 

0 

46 

0 

51 

43 

0 

19 

0 

23 

0 

26 

0 

30 

0 

34 

0 38 

0 

42 

0 

46 

0 

51 

44 

0 

19 

0 

23 

0 

27 

0 

30 

0 

34 

0 38 

0 

43 

0 

47 

0 

52 

45 

0 

19 

0 

23 

0 

27 

0 

31 

0 

35 

0 39 

0 

43 

0 

47 

0 

52 

46 

0 

19 

0 

23 

0 

27 

0 

31 

0 

35 

0 39 

0 

44 

0 

48 

0 

53 

47 

0 

20 

0 

23 

0 

27 

0 

31 

0 

35 

0 40 

0 

44 

0 

49 

0 

54 

48 

0 

20 

0 

23 

0 

27 

0 

31 

0 

35 

0 40 

0 

45 

0 

50 

0 

55 

49 

0 

21 

0 

24 

0 

28 

0 

32 

0 

36 

0 41 

0 

45 

0 

51 

0 

57 

50 

0 

21 

0 

24 

0 

28 

0 

32 

0 

36 

0 41 

0 

46 

0 

52 

0 

58 

51 

0 

21 

0 

24 

0 

28 

0 

32 

0 

37 

0 42 

0 

47 

0 

53 

0 

59 

52 

0 

22 

0 

25 

0 

29 

0 

33 

0 

37 

0 42 

0 

48 

0 

54 

1 

00 

53 

0 

22 

0 

25 

0 

29 

0 

33 

0 

38 

0 43 

0 

49 

0 

55 

1 

01 

54 

0 

23 

0 

26 

0 

30 

0 

34 

0 

39 

0 44 

0 

50 

0 

50 

1 

02 

55 

0 

23 

0 

26 

0 

30 

0 

35 

0 

40 

0 45 

0 

51 

0 

57 

1 

03 

56 

0 

24 

0 

27 

0 

31 

0 

30 

0 

41 

0 46 

0 

52 

0 

58 

1 

04 

57 

0 

24 

0 

28 

0 

32 

0 

37 

0 

42 

0 48 

0 

54 

1 

00 

1 

06 

53 

0 

25 

0 

29 

0 

33 

0 

38 

0 

44 

0 50 

0 

55 

1 

02 

1 

08 

59 

0 

26 

0 

30 

0 

34 

0 

39 

0 

45 

0 51 

0 

57 

1 

04 

1 

10 

60 

0 

27 

0 

31 

0 

35 

0 

40 

0 

46 

0 52 

0 

59 

1 

06 

1 

13 

61 

0 

27 

0 

31 

0 

36 

0 

41 

0 

47 

0 54 

1 

01 

1 

08 

1 

15 

62 

0 

28 

0 

32 

0 

37 

0 

42 

0 

49 

0 56 

1 

03 

1 

10 

1 

18 

63 

0 

29 

0 

33 

0 

39 

0 

44 

0 

51 

0 58 

1 

05 

1 

L 

12 

1 

21 

64 

0 

29 

0 

34 

0 

40 

0 

46 

0 

53 

1 00 

1 

07 

1 

14 

1 

24 

on 

0 

30 

0 

35 

0 

41 

0 

48 

0 

55 

1 02 

1 

09 

1 

17 

1 

27 

66 

0 

31 

0 

37 

0 

43 

0 

50 

0 

58 

1 05 

1 

12 

1 

21 

1 

31 

67 

0 

33 

0 

38 

0 

45 

0 

53 

i 

00 

1 07 

1 

16 

1 

25 

1 

35 

68 

0 

34 

0 

40 

0 

48 

0 

55 

1 

02 

1 10 

1 

19 

1 

30 

1 

39 

69 

0 

36 

0 

42 

0 

50 

0 

58 

1 

05 

1 13 

1 

23 

1 

34 

1 

44 

10 

0 

38 

0 

44 

0 

52 

1 

00 

1 

08 

1 17 

1 

28 

1 

39 

1 

50 1 

71 

0 

40 

0 

46 

0 

55 

1 

03 

1 

12 

1 22 

1 

32 

1 

44 

1 

56 [ 

72 

0 

42 

0 

49 

0 

58 

1 

06 

1 

16 

1 27 

1 

38 

1 

50 1 

2 

J2U 



































TADI.E of MERIDIONAL PARTS. 


95 


Tit'fool IQ] 201 30 1 40j 50 1 GJ| 70 ] 80| QO| I0o| ILO| 130 ] 130 


0 

0 

60 

120 

180 

240 

300 

361 

421 

482 

542 

603 

664 

725 

787 

] 

1 

61 

121 

181 

241 

301 

362 

422 

483 

543 

604 

665 

726 

788 

2 

2 

62 

122 

182 

242 

302 

363 

423 

484 

544 

605 

666 

727 

789 

3 

3 

63 

123 

183 

243 

303 

364 

424 

485 

545 

606 

667 

728 

790 

4 

4 

64 

124 

184 

244 

304 

365 

425 

486 

546 

607 

668 

729 

791 

5 

5 

65 

125 

185 

245 

305 

366 

426 

487 

547 

608 

669 

730 

792 

6 

6 

66 

126 

186 

246 

306 

367 

427 

488 

548 

609 

670 

731 

793 

7 

7 

67 

127 

187 

247 

307 

368 

428 

489 

549 

610 

671 

732 

794 

8 

8 

68 

128 

188 

248 

308 

369 

429 

490 

550 

611 

672 

734 

795 

9i 9 

69 

129 

189 

249 

309 

370 

430 

491 

551 

612 

673 

735 

796 

10 

10 

70 

130 

190 

250 

310 

371 

431 

492 

552 

613 

664 

736 

797 

11 

11 

71 

131 

191 

251 

311 

372 

432 

493 

553 

614 

675 

737 

798 

12 

12 

72 

132 

192 

252 

312 

373 

433 

494 

554 

615 

676 

738 

799 

13 

13 

73 

133 

193 

253 

313 

374 

434 

495 

555 

616 

677 

739 

800 

14 

14 

74 

134 

194 

254 

314 

375 

435 

496 

556 

617 

678 

740 

801 

15 

15 

75 

135 

195 

255 

315 

376 

436 

497 

557 

618 

679 

741 

802 

16 

16 

76 

136 

196 

256 

316 

377 

437 

498 

558 

619 

680 

742 

803 

17 

17 

77 

137 

197 

257 

317 

378 

438 

499 

559 

620 

681 

743 

804 

18 

18 

78 

138 

198 

258 

318 

379 

439 

500 

560 

621 

682 

744 

805 

19 

19 

79 

139 

199 

259 

319 

380 

440 

501 

561 

622 

683 

745 

806 

20 

20 

80 

140 

200 

260 

320 

381 

441 

502 

562 

623 

684 

746 

807 

21 

21 

81 

141 

201 

261 

321 

382 

442 

503 

563 

624 

685 

747 

808 

22 

22 

82 

142 

202 

262 

322 

383 

443 

504 

564 

625 

687 

748 

809 

23 

23 

83 

143 

203 

263 

323 

384 

444 

505 

565 

626 

688 

749 

810 

24 

24 

84 

144 

204 

264 

324 

385 

445 

506 

567 

627 

689 

750 

811 

25 

25 

85 

145 

205 

265 

325 

386 

446 

507 

568 

628 

690 

751 

812 

26 

26 

86 

146 

206 

266 

326 

387 

447 

508 

569 

629 

691 

752 

813 

27 

27 

87 

147 

207 

267 

327 

388 

448 

509 

570 

631 

692 

753 

815 

28 

28 

88 

148 

208 

268 

328 

389 

449 

510 

571 

632 

693 

754 

816 

29 

29 

89 

149 

209 

269 

330 

390 

450 

511 

572 

633 

694 

755 

817 

30 

30 

90 

150 

210 

270 

331 

391 

451 

512 

573 

634 

695 

756 

818 

31 

31 

91 

151 

211 

271 

332 

3S2 

452 

513 

574 

635 

696 

757 

819 

32 

32 

92 

152 

212 

272 

333 

393 

453 

514 

575 

636 

697 

758 

820 

33 

33 

93 

153 

213 

273 

334 

394 

454 

515 

576 

637 

698 

759 

821 

34 

34 

94 

154 

214 

274 

335 

395 

455 

516 

577 

638 

699 

760 

822 

35 

35 

95 

155 

215 

275 

336 

396 

456 

517 

578 

639 

700 

761 

823 

36 

36 

96 

156 

216 

276 

337 

397 

457 

518 

579 

640 

701 

762 

824 

37 

37 

97 

157 

217 

277 

338 

398 

458 

519 

580 

641 

702 

763 

825 

38 

38 

98 

158 

218 

278 

339 

39£ 

459 

520 

581 

642 

703 

764 

826 

39 

39 

99 

159 

219 

279 

340 

400 

460 

521 

582 

643 

704 

765 

827 

40 

40 

100 

160 

220 

280 

341 

401 

461 

522 

583 

644 

705 

766 

828 

41 

41 

101 

161 

221 

281 

342 

402 

462 

523 

584 

645 

706 

767 

829 

42 

42 

102 

162 

222 

282 

343 

403 

463 

524 

585 

646 

707 

768 

830 

43 

43 

103 

163 

223 

283 

344 

404 

464 

525 

586 

647 

708 

769 

831 

41 

44 

104 

164 

224 

284 

345 

405 

465 

526 

587 

648 

709 

770 

832 

45 

45 

105 

165 

225 

285 

346 

406 

466 

527 

588 

649 

710 

771 

833 

46 

46 

106 

166 

226 

286 

347 

407 

467 

528 

589 

650 

711 

772 

834 

47 

47 

107 

167 

227 

287 

348 

408 

468 

529 

590 

651 

712 

773 

835 

48 

48 

108 

168 

228 

288 

349 

409 

469 

530 

591 

652 

713 

774 

836 

49 

49 

109 

169 

229 

289 

350 

410 

470 

531 

592 

653 

714 

775 

837 

50 

50 

110 

170 

230 

290 

351 

411 

471 

532 

593 

654 

715 

777 

838 

51 

51 

111 

17] 

231 

291 

352 

412 

472 

533 

594 

655 

716 

778 

839 

52 

52i 

112 

172 

232 

292 

353 

413 

473 

534 

595 

656 

717 

779 

840 

53! 

53 

113 

173 

233 

293 

354 

414 

474 

535 

596 

657 

718 

780 

841 

54i 

54 

114 

174 

234 

294 

355 

415 

476 

536 

597 

658 

719 

781 

842 

55 

55 

115 

175 

235 

295 

356 

416 

477 

537 

598 

659 

720 

782 

843 

66 

56 

116 

176 

236 

296 

357 

417 

478 

538 

599 

660 

721 

783 

844 

57 

57 

117 

177 

237 

297 

358 

418 

479 

539 

600 

661 

722 

784 

845 

58 

58 

118 

178 

238 

298 

359 

419 

480 

540 

601 

662 

723 

785 

846 

591 

59 

119 

179 

239, 

299 

360 

420 

481 

541 

602 

603 

724 

786 

847 
















































!>6 


TABLE OF MERIDIONAL PARTS. 


M. i 1401 1501 16Q| 17°{ 18Q| 19Q[ 2QQ| 2jQ| 22Q| 23Q| 24Q| W ~>\ 26Q[ 2V~o 


0 

848 

910 

973 

1035 

1098 

1161 

1225 

1289 

1354| 

1419 

1484 

1550 

1616 

1684 

1 

850 

911 

974 

36 

99 

63 

26 

90 

55 

20 

85 

51 

18 

85 

2 

851 

913 

975 

37 

1100 

64 

27 

91 

56 

21 

86 

52 

19 

86 

3 

852 

914 

976 

38 

01 

65 

28 

92 

57 

22 

87 

53 

20 

87 

4 

853 

915 

977 

39 

02 

66 

29 

93 

58 

23 

88 

54 

21 

88 

5 

854 

916 

978 

41 

03 

67 

30 

95 

59 

24 

90 

56 

22 

89 

6 

855 

917 

979 

42 

05 

68 

32 

96 

60 

25 

91 

57 

23 

90 

7 

856 

918 

980 

43 

06 

69 

33 

97 

61 

26 

92 

58 

24 

91 

8 

857 

919 

981 

44 

07 

70 

34 

98 

62 

27 

93 

59 

25 

93 

9 

858 

920 

982 

45 

08 

71 

35 

99 

63 

28 

94 

60 

26 

94 

10 

859 

921 

983 

1046 

1109 

1172 

1236 

1300 

1364 

1430 

1195 

1561 

1628 

1695 j 

11 

860 

922 

984 

47 

10 

73 

37 

01 

66 

31 

96 

62 

29 

96 

12 

861 

923 

985 

48 

11 

74 

38 

02 

67 

32 

97 

63 

30 

97 

13 

862 

924 

986 

49 

12 

75 

39 

03 

68 

33 

98 

64 

31 

98 

14 

863 

925 

987 

50 

13 

76 

40 

04 

69 

34 

99 

65 

32 

99 

15 

864 

926 

988 

51 

14 

77 

41 

05 

70 

35 

1500 

67 

33 

1700 

16 

865 

927 

989 

52 

15 

78 

42 

06 

71 

36 

02 

68 

34 

01 

17 

866 

928 

990 

53 

16 

79 

43 

07 

72 

37 

03 

69 

35 

03 

18 

867 

929 

991 

54 

17 

81 

44 

08 

73 

38 

04 

70 

37 

04 

19 

868 

930 

993 

55 

18 

82 

45 

10 

74 

39 

05 

71 

38 

05 

20 

869 

931 

994 

1056 

1119 

1183 

1246 

1311 

1375 

1440 

1506 

1572 

1639 

1706 

21 

870 

932 

995 

57 

20 

84 

48 

12 

76 

41 

07 

73 

40 

07 

22 

871 

933 

996 

58 

21 

85 

49 

13 

77 

43 

08 

74 

41 

08 

23 

872 

934 

997 

59 

22 

86 

50 

14 

79 

44 

09 

75 

42 

09 

24 

873 

935 

998 

60 

23 

87 

51 

15 

80 

45 

10 

77 

43 

11 

25 

874 

936 

999 

61 

25 

88 

52 

16 

81 

46 

11 

78 

44 

12 

26 

875 

937 

1000 

63 

26 

8§ 

53 

17 

82 

47 

13 

79 

45 

13 

27 

876 

938 

1001 

64 

27 

90 

54 

18 

83 

48 

14 

80 

47 

14 

28 

877 

939 

1002 

65 

28 

91 

55 

19 

84 

49 

15 

81 

48 

15 

29 

878 

941 

1003 

66 

29 

92 

56 

20 

85 

50 

16 

82 

49 

16 

30 

879 

942 

1004 

1067 

1130 

1193 

1257 

1321 

1386 

1451 

1517 

1583 

1650 

1717 

31 

880 

943 

05 

68 

31 

94 

58 

22 

87 

52 

18 

84 

51 

18 

32 

882 

944 

06 

69 

32 

95 

59 

24 

88 

53 

19 

85 

52 

20 

33 

883 

945 

07 

70 

33 

96 

60 

25 

89 

55 

20 

86 

53 

21 

34 

884 

946 

08 

71 

34 

98 

61 

26 

90 

56 

21 

88 

54 

22 

35 

885 

947 

09 

72 

35 

99 

62 

27 

92 

57 

22 

89 

56 

23 

36 

886 

948 

10 

73 

36 

1200 

64 

28 

93 

58 

24 

90 

57 

24 

37 

887 

949 

11 

74 

37 

01 

65 

29 

94 

59 

25 

91 

58 

25 

38 

888 

950 

12 

75 

38 

02 

66 

30 

95 

60 

26 

92 

59 

26 

39 

889 

951 

13 

76 

39 

03 

67 

31 

96 

61 

27 

93 

60 

27 

40 

890 

952 

1014 

1077 

1140 

1204 

1268 

1332 

1397 

1462 

1528 

1594 

1661 

1729 

41 

891 

953 

15 

78 

41 

05 

69 

33 

98 

63 

29 

96 

62 

30 

42 

892 

954 

16 

79 

42 

06 

70 

34 

99 

64 

30 

97 

63 

31 

43 

893 

955 

18 

80 

44 

07 

71 

35 

1400 

65 

31 

98 

64 

32 

44 

894 

956 

19 

81 

45 

08 

72 

36 

01 

67 

32 

99 

66 

33 

45 

895 

957 

20 

82 

46 

09 

73 

38 

02 

68 

33 

1600 

67 

34 

46 

896 

958 

21 

84 

47 

10 

74 

39 

03 

69 

35 

01 

68 

35 

47 

897 

959 

22 

85 

48 

11 

75 

40 

05 

70 

36 

02 

69 

36 

48 

898 

960 

23 

86 

49 

12 

76 

41 

06 

71 

37 

03 

70 

38 

49 

899 

961 

24 

87 

50 

13 

77 

42 

07 

72 

38 

04 

71 

39 

50 

900 

962 

1025 

1088 

1151 

1215 

1278 

1343 

1408 

1473 

1539 

1605 

1672 

1740 

51 

901 

963 

26 

89 

52 

16 

80 

44 

09 

74 

40 

06 

73 

41 

52 

902 

964 

27 

90 

53 

17 

81 

45 

10 

75 

41 

08 

75 

42 

53 

903 

965 

28 

91 

54 

18 

82 

46 

11 

76 

42 

09 

76 

43 

54 

904 

966 

29 

92 

55 

19 

83 

47 

12 

77 

43 

10 

77 

44 

55 

905 

968 

30 

93 

56 

20 

84 

48 

13 

79 

44 

11 

78 

46 

56 

906 

969 

31 

94 

57 

21 

85 

49 

14 

80 

46 

12 

79 

47 

57 

907 

970 

32 

95 

58 

22 

86 

50 

15 

81 

47 

13 

80 

48 

58 

908 

971 

33 

96 

59 

23 

87 

52 

16 

82 

48 

14 

81 

49 

59 

909 

972 

34 97 

60 

24 

88 

53 

18 

83 

49 

15 

82 

50 










































TABLE OF MERIDIONAL PARTtt. 


97 


M. 1 28Q| 0901 3qo| 3|Q| 3301 330] 3401 3501 3f>o[ 3701 38O|~30Oj 400| 410 


0 

1751 

1819 

1888 

1958 

2028 

2100 

2171 

2244 

2318 

2393 

2468 

2545 

2623 2702 

1 

52 

21 

90 

59 

30 

01 

73 

46 

19 

94 

70 

46 

24 

03 

2 

53 

22 

91 

60 

31 

02 

74 

47 

20 

95 

71 

48 

25 

04 

3 

55 

23 

92 

62 

32 

03 

75 

48 

22 

96 

72 

49 

27 

06 

4 

56 

24 

93 

63 

33 

04 

76 

49 

23 

98 

73 

50 

28 

07 

5 

57 

25 

94 

64 

34 

05 

78 

50 

24 

99 

75 

51 

29 

08 

6 

58 

26 

95 

65 

35 

07 

79 

52 

25 

2400 

76 

53 

31 

10 

7 

59 

27 

96 

66 

37 

08 

80 

53 

27 

01 

77 

54 

32 

11 

8 

60 

29 

98 

67 

38 

09 

81 

54 

28 

03 

78 

55 

33 

12 

9 

61 

30 

99 

69 

39 

10 

82 

55 

29 

04 

80 

57 

34 

14 

10 

1762 

1831 

1900 

1970 

2040 

2111 

2184 

2257 

2330 

2405 

2481 

2558 

2636 

2715 

11 

64 

32 

01 

71 

41 

13 

85 

58 

32 

06 

82 

59 

37 

16 

12 

65 

33 

02 

72 

43 

14 

86 

59 

33 

08 

84 

60 

38 

18 

13 

66 

34 

03 

73 

44 

15 

87 

60 

34 

09 

85 

62 

40 

19 

14 

67 

35 

05 

74 

45 

16 

88 

61 

35 

10 

86 

63 

41 

20 

15 

68 

37 

06 

76 

46 

17 

90 

63 

37 

11 

87 

64 

42 

22 

16 

69 

38 

07 

77 

47 

19 

91 

64 

38 

13 

89 

66 

44 

23 

17 

70 

39 

08 

78 

48 

20 

92 

65 

39 

14 

90 

67 

45 

24 

18 

72 

40 

09 

79 

50 

21 

93 

66 

40 

15 

91 

68 

46 

26 

19 

73 

41 

10 

80 

51 

22 

94 

68 

42 

16 

92 

69 

48 

27 

20 

1774 

1842 

1912 

1981 

2052 

2123 

2196 

2269 

2343 

2418 

2494 

2571 

2649 

2728 

21 

75 

43 

13 

83 

53 

25 

97 

70 

44 

19 

95 

72 

50 

29 

22 

76 

45 

14 

84 

54 

26 

98 

71 

45 

20 

96 

73 

51 

31 

23 

77 

46 

15 

85 

56 

27 

99 

72 

46 

22 

98 

75 

53 

32 

24 

78 

47 

16 

86 

57 

28 

2200 

74 

48 

23 

99 

76 

54 

33 

25 

80 

48 

17 

87 

58 

29 

02 

75 

49 

24 

2500 

77 

55 

35 

26 

81 

49 

18 

88 

59 

31 

03 

76 

50 

25 

01 

78 

57 

36 

27 

82 

50 

20 

90 

60 

32 

04 

77 

51 

27 

03 

80 

58 

37 

28 

83 

62 

21 

91 

61 

33 

05 

79 

53 

28 

04 

81 

59 

39 

29 

84 

53 

22 

92 

63 

34 

07 

80 

54 

29 

05 

82 

61 

40 

30 

1785 

1854 

1923 

1993 

2064 

2135 

2208 

2281 

2355 

2430 

2506 

2584 

2662 

i M2 

31 

86 

55 

24 

94 

65 

37 

09 

82 

56 

32 

08 

85 

63 

43 

32 

87 

56 

25 

95 

66 

38 

10 

83 

58 

33 

09 

86 

65 

44 

33 

89 

57 

27 

97 

67 

39 

11 

85 

59 

34 

10 

88 

66 

46 

34 

90 

58 

28 

98 

69 

40 

13 

86 

60 

35 

12 

89 

6: 

47 

35 

91 

60 

29 

99 

70 

41 

14 

87 

61 

37 

13 

90 

6!- 

48 

36 

92 

61 

30 

2000 

71 

43 

15 

88 

63 

38 

14 

91 

7./ 

50 

37 

93 

62 

31 

01 

72 

44 

16 

90 

64 

39 

15 

93 

71 

51 

38 

94 

63 

32 

02 

73 

45 

17 

91 

65 

40 

1? 

94 

1 1 

52 

39 

95 

64 

34 

04 

75 

46 

19 

92 

66 

42 

18 

95 

7 1 

54 

40 

1797 

1865 

1935 

2005 

2076 

2147 

2220 

2293 

2368 

2443 

2519 

2597 

2675 

2755 

41 

98 

66 

36 

06 

77 

49 

21 

95 

69 

44 

21 

98 

76 

56 

42 

99 

68 

37 

07 

78 

50 

22 

96 

70 

45 

22 

99 

78 

58 

43 

1800 

69 

38 

08 

79 

51 

24 

97 

71 

47 

23 

2600 

79 

59 

44 

01 

70 

39 

10 

80 

52 

25 

98 

73 

48 

24 

02 

80 

60 

45 

02 

71 

41 

11 

82 

53 

26 

99 

74 

49 

26 

03 

82 

62 

46 

03 

72 

42 

12 

83 

55 

27 

2301 

75 

51 

27 

04 

83 

63 

47 

05 

73 

43 

13 

84 

56 

28 

02 

76 

52 

28 

06 

84 

64 

48 

06 

75 

44 

14 

85 

57 

30 

03 

78 

53 

30 

07 

86 

60 

49 

07 

76 

45 

15 

86 

58 

31 

04 

79 

54 

31 

08 

87 

67 

50 

1808 

1877 

1946 

2017 

2088 

2159 

2232 

2306 

2380 

2456 

2532 

2610 

2688 

2768 

61 

09 

78 

48 

18 

89 

61 

33 

07 

31 

57 

33 

11 

90 

70 

62 

10 

79 

49 

'9 

90 

62 

35 

08 

83 

58 

35 

12 

91 

71 

63 

11 

80 

50 

20 

91 

63 

36 

09 

84 

59 

36 

14 

92 

72 

64 

1« 

81 

51 

21 

92 

64 

37 

11 

85 

61 

37 

15 

94 

74 

65 

1 

83 

52 

22 

94 

65 

38 

12 

86 

62 

38 

16 

95 

75 

56 

15 

84 

53 

24 

95 

67 

39 

13 

88 

63 

40 

17 

96 

76 

57 

16 

85 

55 

25 

96 

68 

41 

14 

89 

64 

41 

19 

98 

78 

58 

17 

86 

56 

26 

97 

69 

42 

16 

90 

66 

42 

20 

99 

79 

69 

18 

87 

67 

27 

98 

70 

43 

17 

91 

67 

44 

21 

2700 

80 










































9d TABLE OF MERIDIONAL FARTS. 


M. 

420 

4301 

4401 

450] 

460] 

4701 

480j 

490] 

50<o 

510 

520) 

5301 

540 

550 

0 

2782 2863 

2946 

3030 

3116 

3203 

329213382 

3474 

3569 

3665 

376413865 

3968 

1 

83 

64 

47 

31 

17 

04 

931 

84 

76 

70 

67 

65 

67 

70 

2 

84 

66 

49 

33 

18 

06 

95 

85 

78- 

72 

68 

67 

68 

71 

3 

86 

G7 

50 

34 

20 

07 

96 

87 

79 

74 

70 

69 

70 

73 

4 

87 

69 

51 

36 

21 

09 

98 

88 

81 

75 

72 

70 

71 

75 

5 

88 

70 

53 

37 

23 

10 

99 

90 

82 

77 

73 

72 

73 

77 

6 

90 

71 

54 

38 

24 

12 

3301 

91 

S4 

78 

75 

74 

75 

78 

7 

91 

73 

56 

40 

26 

13 

02 

93 

85 

80 

77 

75 

77 

80 

8 

92 

74 

57 

41 

27 

14 

03 

94 

87 

82 

78 

77 

78 

82 

9 

94 

75 

58 

43 

29 

16 

05 

96 

88 

83 

80 

79 

80 

84 

<0 

2795 

2877 

2960 

3044 

3130 

3217 

3306 

3397 

3490 

3585 

3681 

37S0 

3882 

3985 

1 L 

97 

78 

61 

46 

31 

19 

08 

99 

92 

86 

83 

82 

83 

87 

1 2 

98 

80 

63 

47 

33 

20 

09 

3400 

93 

88 

85 

84 

85 

89 

13 

99 

81 

64 

48 

34 

22 

11 

02 

95 

90 

86 

85 

87 

91 

14 

2801 

82 

65 

50 

36 

23 

12 

03 

96 

91 

88 

87 

89 

92 

15 

02 

84 

67 

51 

37 

25 

14 

05 

98 

93 

90 

89 

90 

94 

1 G 

03 

85 

68 

53 

39 

26 

16 

07 

99 

94 

91 

90 

92 

96 

17 

05 

86 

70 

54 

40 

28 

17 

08 

3501 

96 

93 

92 

94 

98 

18 

06 

88 

71 

55 

42 

29 

19 

10 

03 

98 

95 

94 

95 

99 

19 

07 

89 

72 

57 

43 

31 

20 

11 

04 

99 

96 

95 

97 

4001 

20 

2809 

2S91 

2974 

3058 

3144 

3232 

3322 

3413 

3506 

3601 

3698 

3797 

3899 

4003 

21 

10 

92 

75 

60 

46 

34 

24 

14 

07 

02 

99 

99 

3991 

05 

22 

11 

93 

76 

61 

47 

35 

25 

16 

09 

04 

3701 

3800 

02 

0 G 

23 

13 

95 

78 

63 

49 

37 

26 

17 

10 

06 

03 

02 

04 

OS 

24 

14 

96 

79 

64 

50 

38 

28 

19 

12 

07 

04 

04 

06 

10 

25 

15 

97 

81 

65 

52 

40 

29 

20 

14 

09 

06 

06 

07 

12 

26 

17 

99 

82 

67 

53 

41 

31 

oo 

»*<v 

15 

10 

07 

07 

09 

14 

27 

18 

2900 

83 

68 

55 

42 

32 

23 

17 

12 

09 

09 

11 

15 

28 

20 

02 

85 

70 

56 

44 

34 

25 

18 

14 

11 

11 

13 

17 

29 

21 

03 

86 

71 

57 

45 

35 

27 

20 

15 

13 

12 

14 

19 

30 

2822 

2904 

2988 

3073 

3159 

3247 

3337 

3428 

3521 

3617 

3714 

3814 

3916 

4021 

31 

24 

06 

89 

74 

60 

48 

38 

30 

23 

18 

16 

16 

18 

22 

32 

25 

07 

91 

75 

62 

50 

40 

31 

25 

20 

17 

17 

19 

24 

33 

26 

08 

92 

77 

63 

51 

41 

33 

26 

22 

19 

19 

21 

26 

34 

28 

10 

93 

78 

65 

53 

43 

34 

28 

23 

21 

21 

22 

28 

35 

29 

11 

95 

80 

66 

54 

44 

36 

29 

25 

22 

22 

25 

29 

36 

30 

13 

96 

81 

68 

56 

46 

37 

31 

26 

24 

24 

26 

31 

37 

32 

14 

98 

83 

69 

57 

47 

39 

32 

28 

26 

26 

28 

33 

38 

33 

15 

99 

84 

71 

59 

49 

40 

34 

30 

27 

27 

30 

35 

39 

34 

17 

3000 

85 

72 

60 

50 

42 

36 

31 

29 

29 

32 

37 

40 

2836 

2918 

3002 

3087 

3173 

3262 

3352 

3443 

3537 

3633 

3731 

3331 

3933 

1038 

41 

37 

19 

03 

88 

75 

63 

53 

45 

39 

34 

32 

32 

35 

40 

42 

39 

21 

05 

90 

76 

65 

55 

47 

40 

36 

34 

34 

37 

42 

43 

40 

22 

06 

91 

78 

66 

56 

48 

42 

38 

36 

36 

38 

44 

44 

41 

24 

07 

93 

79 

68 

58 

50 

43 

39 

37 

38 

40 

45 

45 

43 

25 

09 

94 

81 

69 

59 

51 

45 

41 

39 

39 

42 

47 

46 

44 

26 

10 

95 

82 

71 

61 

53 

47 

43 

41 

41 

44 

49 

47 

45 

28 

12 

97 

84 

72 

62 

54 

48 

44 

42 

43 

45 

51 

48 

47 

29 

13 

98 

85 

74 

64 

56 

50 

46 

44 

44 

47 

52 

49 

48 

31 

14 

3100 

87 

75 

65 

57 

51 

47 

46 

46 

49 

51 

50 

2849 

2932 

3016 

3101 

3188 

3277 

3367 

3459 

3553 

3649 

3747 

384 S 

3951 

4056 

51 

51 

33 

17 

03 

90 

78 

68 

60 

55 

51 

49 

49 

52 

58 

52 

52 

35 

19 

04 

91 

80 

70 

62 

56 

52 

50 

51 

54 

GO 

53 

54 

36 

20 

05 

92 

81 

71 

64 

58 

54 

52 

53 

56 

61 

54 

55 

37 

21 

07 

94 

83 

73 

65 

59 

55 

54 

54 

58 

63 

55 

56 

39 

23 

08 

95 

84 

74 

67 

61 

57 

55 

56 

59 

65 

56 

58 

40 

24 

10 

97 

86 

76 

68 

62 

59 

57 

58 

61 

C7 

57 

59 

42 

26 

11 

98 

87 

78 

70 

64 

60 

59 

60 

G3 

69 

58 

60 

43 

27 

13 

3200 

89 

79 

71 

66 

62 

60 

61 

64 

70 

59 

62 

44 

29 

14 

01 

90 

81 

73 

67 

64 

62 

63 

66 

72 
















































TABLE OF MEI.IDIONAL PARTS. 


99 


M. | 5601 5701 5801 5901 60O| 61o| 620| 630) 64°| 650) 660) 670) 08O| 690 


0 4074 

4183 

4294 

4409 

4527 

4649 

4775 

49051 

5039 5179 

5324 

5474 

5631 

5795 

ll 

76 

84 

96 

11 

29 

51 

77 

07 

42 

81 

26 

77 

33 

9 7 

2 

77 

86 

98 

13 

31 

53 

79 

09 

44 

84 

28 

79 

36 

5800 

3 

79 

88 

4300 

15 

33 

55 

81 

12 

46 

86 

3” 

82 

39 

03 

4' 

81 

90 

02 

17 

35 

57 

V'r 

14 

49 

88 

33 

84 

42 

06 

5‘ 

83 

92 

04 

19 

37 

60 

86 

16 

51 

91 

36 

87 

44 

09 

61 

85 

94 

06 

21 

39 

62 

88 

18 

53 

93 

38 

89 

47 

11 

7 

86 

95 

08 

23 

41 

64 

90 

20 

55 

95 

41 

92 

50 

14 

8 

88 

97 

09 

25 

43 

66 

92 

23 

58 

98 

43 

95 

52 

17 

9 

90 

99 

11 

27 

45 

68 

94 

25 

60 

5200 

46 

97 

55 

20 

10 

4092 

4201 

4313 

4429 

4547 

4670 

4796 

4927 

5062 1 

5203 

5348 

5500 

5658 

5823 

11 

94 

03 

15 

31 

49 

72 

98 

29 

65 

05 

51 

02 

60 

25 

12 

95 

05 

17 

33 

51 

74 

4801 

31 

67 

07 

53 

05 

63 

28 

13 

97 

07 

19 

34 

53 

76 

03 

34 

69 

10 

56 

07 

66 

31 

14 

99 

08 

21 

36 

55 

78 

05 

36 

71 

12 

58 

10 

68 

34 

15 

4101 

10 

23 

38 

57 

80 

07 

38 

74 

14 

61 

13 

71 

37 

16 

03 

12 

25 

40 

59 

82 

09 

40 

76 

17 

63 

15 

74 

39 

17 

04 

14 

27 

42 

62 

84 

11 

43 

78 

19 

66 

18 

76 

42 

18 

06 

16 

28 

44 

64 

87 

14 

45 

81 

22 

68 

20 

79 

45 

19 

08 

18 

30 

46 

66 

89 

16 

47 

83 

24 

71 

23 

82 

48 

20 

4110 

4220 

4332 

4448 

4568 

4691 

4818 

4949 

5085 

5226 

5373 

5526 

5685 

5851 

21 

12 

21 

34 

50 

70 

93 

20 

51 

88 

29 

76 

28 

87 

54 

22 

13 

23 

36 

52 

72 

95 

22 

54 

90 

31 

78 

31 

90 

56 

23 

15 

25 

38 

54 

74 

97 

24 

56 

92 

34 

80 

33 

93 

59 

24 

17 

27 

40 

56 

76 

99 

26 

58 

95 

36 

83 

36 

95 

62 

25 

19 

29 

42 

58 

78 

4701 

29 

60 

97 

38 

85 

39 

98 

65 

26 

21 

31 

44 

60 

80 

03 

31 

63 

99 

41 

88 

41 

5701 

68 

27 

00 

/<*<■* 

32 

46 

62 

82 

05 

33 

65 

5102 

43 

90 

44 

04 

71 

28 

24 

34 

47 

64 

84 

07 

35 

67 

04 

46 

93 

46 

06 

74 

29 

26 

36 

49 

66 

86 

10 

37 

69 

06 

48 

95 

49 

09 

76 

30 

4128 

4238 

4351 

4468 

4588 

4712 

4839 

4972 

5108 

5250 

5398 

5552 

5712 

5879 

31 

30 

40 

53 

70 

90 

14 

42 

74 

11 

53 

5401 

54 

15 

82 

32 

32 

42 

55 

72 

92 

16 

44 

76 

13 

55 

03 

57 

17 

85 

33 

33 

44 

57 

74 

94 

18 

46 

78 

15 

58 

06 

59 

20 

88 

34 

35 

46 

59 

76 

96 

20 

48 

81 

18 

60 

08 

62 

23 

91 

35 

37 

47 

61 

78 

98 

22 

50 

83 

20 

63 

11 

65 

25 

94 

36 

39 

49 

63 

80 

4600 

24 

52 

85 

22 

65 

13 

67 

28 

96 

37 

41 

51 

65 

82 

02 

26 

55 

87 

25 

67 

16 

70 

31 

99 

3S 

42 

53 

67 

84 

04 

28 

57 

90 

27 

70 

18 

73 

34 

5902 

39 

44 

55 

69 

86 

06 

31 

59 

92 

29 

72 

21 

75 

36 

05 

40 

4146 

4257 

4370 

4488 

4608 

4733 

4861 

4994 

5132 

5275 

5423 

5578 

5739 

5908 

41 

48 

£9 

72 

90 

10 

35 

63 

96 

34 

77 

26 

80 

42 

11 

42 

50 

GO 

74 

92 

12 

37 

65 

99 

36 

80 

28 

83 

45 

14 

43 

52 

62 

76 

94 

14 

39 

68 

5001 

39 

82 

31 

86 

47 

17 

44 

53 

64 

78 

95 

16 

41 

70 

03 

41 

84 

33 

88 

50 

19 

45 

55 

66 

80 

97 

18 

43 

72 

05 

43 

87 

36 

91 

53 

22 

46 

57 

68 

82 

99 

20 

45 

74 

08 

46 

89 

38 

94 

56 

25 

47 

59 

70 

84 

4501 

23 

47 

76 

10 

48 

92 

41 

96 

58 

2S 

48 

61 

72 

86 

03 

25 

50 

79 

12 

51 

94 

43 

99 

61 

31 

49 

62 

74 

88 

05 

27 

52 

81 

14 

53 

97 

46 

5602 

64 

34 

50 

4184 

4275 

4390 

4507 

4629 

4754 

4883 

5017 

5155 

5299 

5148 

5604 

5767 

5937 

51 

66 

77 

92 

09 

31 

56 

85 

19 

58 

5301 

51 

07 

70 

40 

52 

68 

79 

94 

11 

33 

58 

87 

21 

60 

04 

54 

10 

72 

43 

53 

70 

81 

96 

13 

35 

60 

90 

23 

62 

06 

56 

12 

75 

46 

54 

72 

83 

98 

15 

3" 

62 

92 

26 

65 

09 

59 

15 

78 

48 

55 

73 

85 

99 

17 

39 

64 

94 

28 

67 

11 

61 

17 

81 

51 

56 

75 

87 

4401 

19 

41 

66 

96 

30 

69 

14 

64 

20 

83 

54 

57 

77 

89 

03 

21 

43 

69 

98 

33 

72 

16 

6G 

23 

86 

57 

58 

79 

91 

05 

23 

45 

71 

4901 

35 

74 

19 

69 

25 

89 

60 

59 

81 

92 

07 

25 

47 

73 

03 

37 

76 

21 

71 

28 

92 

63 


>■ 

















































100 


TAFM.E OF MERIDIONAL PARTS. 


M.| 7(joJ 7io) 7 -zc\ 7 3Q| 74Q| 75°| 760) 77°| 78Q| 79°| 800) 81°1 82° j_83° 


0:5906 0146 

6335 

6534 

674616970 7210 

746717745 

8046 

8375 

8739 

9145 

960G 

1 

60 

49 

38 

38 

49 

74 

14 

72 

49 

51 

81 

45 

53 

14 

O 

** 

72 

52 

41 

41 

53 

78 

18 

76 

54 

56 

87 

52 

60 

22 

3 

75 

55 

45 

45 

57 

82 

22 

81 

59 

61 

93 

58 

67 

31 

4 

78 

58 

48 

48 

60 

86 

27 

85 

64 

67 

98 

65 

74 

39 

5 

81 

61 

51 

52 

64 

90 

31 

90 

69 

72 

8404 

71 

82 

47 

6 

84 

64 

54 

55 

68 

94 

35 

94 

74 

77 

10 

78 

89 

• 

7 

86 

67 

58 

58 

71 

97 

39 

98 

78 

83 

16 

84 

96 

64 

8 

89 

70 

61 

62 

75 

7001 

43 

7503 

83 

88 

22 

91 

9203 

72 

9 

92 

73 

64 

65 

79 

05 

47 

07 

88 

93 

27 

97 

11 

81 

10 

5995 

6177 

6367 

6569 

6782 

7009 

7252 

7512 

7793 

8099 

8433 

8804 

9218 

9689 

11 

98 

80 

71 

72 

86 

13 

56 

16 

98 

8104 

39 

10 

25 

97 

12 

6001 

83 

74 

76 

90 

17 

60 

21 

7803 

09 

45 

17 

33 

9706 

13 

04 

86 

77 

79 

93 

21 

64 

25 

08 

15 

51 

23 

40 

14 

14 

07 

89 

80 

83 

97 

25 

68 

30 

13 

20 

57 

30 

48 

23 

15 

10 

92 

84 

86 

6801 

29 

73 

35 

17 

25 

63 

36 

55 

31 

16 

13 

95 

87 

90 

04 

33 

77 

39 

22 

31 

69 

43 

62 

40 

17 

16 

98 

90 

93 

08 

37 

81 

44 

27 

36 

74 

49 

70 

48 

18 

19 

6201 

94 

96 

12 

41 

85 

48 

32 

41 

80 

56 

77 

57 

19 

22 

05 

97 

6600 

15 

45 

89 

53 

37 

47 

86 

63 

85 

65 

20 

6025 

6208 

6400 

6603 

6819 

7049 

7294 

7557 

7842 

8152 

8492 

8869 

9292 

9774 

21 

28 

11 

03 

07 

23 

52 

98 

62 

47 

58 

98 

76 

9300 

83 

22 

31 

14 

07 

10 

26 

56 

7302 

66 

52 

63 

8504 

83 

07 

91 

23 

34 

17 

10 

14 

30 

60 

06 

71 

57 

68 

10 

89 

15 

9800 

24 

37 

20 

13 

17 

34 

64 

11 

76 

62 

74 

16 

96 

22 

09 

25 

40 

23 

17 

21 

38 

68 

15 

80 

67 

79 

22 

8903 

<10 

17 

26 

43 

26 

20 

24 

41 

72 

19 

85 

72 

85 

28 

09 

38 

26 

27 

46 

30 

23 

28 

45 

76 

23 

89 

77 

90 

34 

16 

45 

35 

28 

49 

33 

27 

31 

49 

80 

28 

94 

82 

96 

40 

23 

53 

44 

29 

52 

36 

30 

35 

53 

84 

32 

98 

87 

8201 

46 

30 

60 

52 

30 

6055 

6239 

6433 

6639 

6856 

7088 

7336 

7603 

7892 

8207 

8552 

8936 

9368 

9861 

31 

58 

42 

37 

42 

60 

92 

40 

08 

97 

12 

58 

43 

76 

70 

32 

61 

45 

40 

46 

64 

96 

45 

12 

7902 

18 

64 

50 

83 

79 

33 

64 

49 

43 

49 

68 

7100 

49 

17 

07 

23 

71 

57 

91 

88 

34 

67 

52 

47 

53 

71 

04 

53 

22 

12 

29 

77 

63 

99 

97 

35 

70 

55 

50 

56 

75 

08 

58 

26 

17 

34 

83 

70 

9407 

9906 

36 

73 

58 

53 

60 

79 

12 

62 

31 

22 

40 

89 

77 

14 

15 

37 

76 

61 

57 

63 

83 

16 

66 

36 

27 

45 

95 

84 

22 

24 

38 

79 

64 

60 

67 

86 

20 

71 

40 

32 

51 

8601 

91 

30 

33 

39 

82 

68 

63 

70 

90 

24 

75 

45 

37 

56 

07 

98 

38 

42 

40 

6085 

6271 

6467 

6674 

6894 

7128 

7379 

7650 

7942 

8262 

8614 

9005 

9445 

9951 

41 

88 

74 

70 

77 

98 

32 

84 

54 

48 

67 

20 

12 

53 

69 

42 

91 

77 

73 

81 

6901 

36 

88 

59 

53 

73 

26 

18 

61 

69 

43 

94 

80 

77 

85 

05 

40 

92 

64 

58 

79 

32 

25 

69 

78 

44 

97 

83 

80 

88 

09 

45 

97 

68 

63 

84 

38 

32 

77 

87 

45 

6100 

87 

83 

92 

13 

49 

7401 

73 

68 

90 

44 

39 

85 

9.196 

46 

04 

90 

87 

95 

17 

53 

06 

78 

73 

95 

51 

46 

93 

10005 

47 

06 

93 

90 

99 

20 

57 

10 

83 

78 

8301 

57 

53 

9501 

10015 

48 

09 

96 

94 

6702 

24 

61 

14 

87 

83 

07 

63 

60 

09 

10024 

49 

12 

99 

97 

06 

28 

65 

19 

92 

89 

12 

69 

67 

17 

10033 

60 

6115 

6303 

6500 

6710 

6932 

7169 

7423 

7697 

7994 

8318 

8676 

9074 

9525 

10043 

51 

18 

06 

04 

13 

36 

73 

27 

7702 

99 

24 

82 

81 

33 

10052 

52 

21 

09 

07 

17 

40 

77 

32 

06 

8004 

29 

88 

88 

41 

10061 

63 

24 

12 

11 

20 

43 

81 

36 

11 

09 

35 

93 

96 

49 

10071 

54 

27 

15 

U 

24 

47 

85 

41 

16 

14 

41 

8701 

9103 

57 

10080 

55 

30 

19 

V 

28 

51 

89 

45 

21 

20 

47 

07 

10 

65 

10089 

56 

33 

22 

21 

31 

55 

94 

49 

25 

25 

52 

14 

17 

73 

10099 

57 

36 

25 

24 

35 

59 

98 

54 

30 

30 

58 

20 

24 

81 

10108 

58 

40 

28 

28 

38 

63 

7202 

58 

35 

35 

64 

26 

31 

89 

10118 

59 

43 

32 

31 

42 

66 

06 

63 

40 

40 

69 

33 

38 

98 

10127 


’# 



































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W. A S. Jones .H6ttKm\.Lowtow. 


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